{"id":365,"date":"2020-07-09T16:56:57","date_gmt":"2020-07-09T16:56:57","guid":{"rendered":"http:\/\/sites.rutgers.edu\/narek-hovsepyan\/?page_id=365"},"modified":"2025-09-25T04:47:32","modified_gmt":"2025-09-25T04:47:32","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h2>Research Interests<\/h2>\n<p>My research lies in the broad area of applied mathematics and analysis of partial differential equations. Of particular interest are questions related to the mathematical aspects of materials science, such as cloaking, metamaterials, and complex media; linear passive systems; (inverse) scattering theory; and nonlinear optics.<\/p>\n<h2 style=\"text-align: left\">Publications and Preprints<\/h2>\n<ul>\n<li style=\"padding-bottom: 4px\">(with M. Ayala, D. Blanco, F. Cakoni and M. Vogelius) On the existence of positive nonlinear transmission eigenvalues in the second-harmonic generation process, in preparation.<\/li>\n<li>(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~vogelius\/\" target=\"_blank\" rel=\"noopener noreferrer\">M. Vogelius<\/a>) Scattering of plane waves, submitted, 2025. <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2509.19716\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv:2509.19716<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~vogelius\/\" target=\"_blank\" rel=\"noopener noreferrer\">M. Vogelius<\/a>) Scattering from analytic and piecewise analytic inhomogeneities, submitted, 2025. <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2507.13986\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv:2507.13986<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~fc292\/\" target=\"_blank\" rel=\"noopener noreferrer\">F. Cakoni<\/a>, <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.mv.helsinki.fi\/home\/lassas\/index.html\" target=\"_blank\" rel=\"noopener noreferrer\">M. Lassas<\/a> and <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~vogelius\/\" target=\"_blank\" rel=\"noopener noreferrer\">M. Vogelius<\/a>) On the lack of external response of nonlinear media in the second-harmonic generation process, <em>SIAM J. Math. Anal.<\/em>, 57, No. 2, pp. 1370-1405, 2025. <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1669700\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> | <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2401.00998\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">On the distribution of Born transmission eigenvalues in the complex plane, <em>Asymptot. Anal.<\/em>,136, No. 1, pp. 27-60, 2024.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/content.iospress.com\/articles\/asymptotic-analysis\/asy231868\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> | <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2304.09470\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~fc292\/\" target=\"_blank\" rel=\"noopener noreferrer\">F. Cakoni<\/a> and <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/sites.math.rutgers.edu\/~vogelius\/\" target=\"_blank\" rel=\"noopener noreferrer\">M. Vogelius<\/a>) Far field broadband approximate cloaking for the Helmholtz equation with a Drude-Lorentz refractive index, <em>J. Math. Pures Appl.<\/em>,\u00a0182, pp. 285-318, 2024..\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0021782423001526\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> | <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2304.09461\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">On the optimal analytic continuation from discrete data, <em>Houst. J. Math.<\/em>, 48, No. 2, pp. 281\u2013293, 2022.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/www.math.uh.edu\/~hjm\/Vol48-2.html\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> | <a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2106.01471\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"http:\/\/web.math.ucsb.edu\/~harutyunyan\/\" target=\"_blank\" rel=\"noopener noreferrer\">D. Harutyunyan<\/a>) On the extreme rays of the cone of 3&#215;3 quasiconvex quadratic forms: extremal determinants vs. extremal and polyconvex forms, <em>Arch. Ration. Mech. Anal.<\/em>, 244, pp. 1-25, 2022.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s00205-021-01724-6\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2102.07334\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.math.temple.edu\/~yury\/\" target=\"_blank\" rel=\"noopener noreferrer\">Y. Grabovsky<\/a>) On the feasibility of extrapolation of the complex electromagnetic permittivity function using Kramers-Kronig relations, <em>SIAM J. Math. Anal.<\/em>, 53, No. 6, pp. 6993\u20137023, 2021.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1369427\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2009.12441\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.math.temple.edu\/~yury\/\" target=\"_blank\" rel=\"noopener noreferrer\">Y. Grabovsky<\/a>) On the commutation properties of finite convolution and differential operators II: sesquicommutation, <em>Results Math<\/em>, 76, No. 3, Article 111, 2021. \u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s00025-021-01412-7\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/1906.02682\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.math.temple.edu\/~yury\/\" target=\"_blank\" rel=\"noopener noreferrer\">Y. Grabovsky<\/a>) On the commutation properties of finite convolution and differential operators I: commutation, <em>Results Math<\/em>, 76, No. 3, Article 112, 2021. \u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s00025-021-01411-8\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/1807.09252\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"http:\/\/www.z-avetisyan.com\/\" target=\"_blank\" rel=\"noopener noreferrer\">Zh. Avetisyan<\/a> and <a style=\"color: #000000;text-decoration: none\" href=\"http:\/\/web.math.ucsb.edu\/~harutyunyan\/\" target=\"_blank\" rel=\"noopener noreferrer\">D. Harutyunyan<\/a>) Rigidity of a thin domain depends on the curvature, size, and boundary conditions, <em>Appl. Math. Opt.<\/em>, 84, pp. 3229\u20133254, 2021.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s00245-021-09746-y\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/2006.08840\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.math.temple.edu\/~yury\/\" target=\"_blank\" rel=\"noopener noreferrer\">Y. Grabovsky<\/a>) Optimal error estimates for analytic continuation in the upper half-plane, <em>Commun. Pure Appl. Math<\/em>, 74, No. 1, pp. 140-171, 2021. \u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1002\/cpa.21901\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/1812.05715\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.math.temple.edu\/~yury\/\" target=\"_blank\" rel=\"noopener noreferrer\">Y. Grabovsky<\/a>) Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces, <em>Inverse Problems<\/em>, 36, No. 3, pp. 035001-035023, 2020. \u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/ab5314\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/1907.13325\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(with <a style=\"color: #000000;text-decoration: none\" href=\"https:\/\/www.hcm.uni-bonn.de\/people\/profile\/juan-j-velazquez\/\" target=\"_blank\" rel=\"noopener noreferrer\">J. J. L. Vel\u00e1zquez<\/a>) Hopf Bifurcation in structural population models, <em>Math. Methods Appl. Sci.<\/em>, 39, No. 18, pp. 5258 &#8211; 5280, 2016. \u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/onlinelibrary.wiley.com\/doi\/abs\/10.1002\/mma.3913\" target=\"_blank\" rel=\"noopener noreferrer\">journal link<\/a> |\u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/arxiv.org\/abs\/1807.08897\" target=\"_blank\" rel=\"noopener noreferrer\">arXiv<\/a><\/li>\n<li style=\"padding-bottom: 4px\">(PhD dissertation) Quantification of Stability of Analytic Continuation with Applications to Electromagnetic Theory, <em>Temple University\u2009ProQuest Dissertations Publishing<\/em>, 2021.\u00a0 \u00a0<a style=\"color: #990000;text-decoration: none\" href=\"https:\/\/www.proquest.com\/docview\/2572595336?pq-origsite=gscholar&amp;fromopenview=true\" target=\"_blank\" rel=\"noopener noreferrer\">link<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Research Interests My research lies in the broad area of applied mathematics and analysis of partial differential equations. Of particular interest are questions related to the mathematical aspects of materials &hellip; <a href=\"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/\" class=\"\">Read More<\/a><\/p>\n","protected":false},"author":21,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-custom.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-365","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Research - Narek Hovsepyan<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Research - Narek Hovsepyan\" \/>\n<meta property=\"og:description\" content=\"Research Interests My research lies in the broad area of applied mathematics and analysis of partial differential equations. 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Of particular interest are questions related to the mathematical aspects of materials &hellip; Read More","og_url":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/","og_site_name":"Narek Hovsepyan","article_modified_time":"2025-09-25T04:47:32+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/","url":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/","name":"Research - Narek Hovsepyan","isPartOf":{"@id":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/#website"},"datePublished":"2020-07-09T16:56:57+00:00","dateModified":"2025-09-25T04:47:32+00:00","breadcrumb":{"@id":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/research\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/"},{"@type":"ListItem","position":2,"name":"Research"}]},{"@type":"WebSite","@id":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/#website","url":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/","name":"Narek Hovsepyan","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links":{"self":[{"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/pages\/365"}],"collection":[{"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/comments?post=365"}],"version-history":[{"count":39,"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/pages\/365\/revisions"}],"predecessor-version":[{"id":601,"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/pages\/365\/revisions\/601"}],"wp:attachment":[{"href":"https:\/\/sites.rutgers.edu\/narek-hovsepyan\/wp-json\/wp\/v2\/media?parent=365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}