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2090-08.pdf | 12.93 MB | Adobe PDF | 見る/開く |
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dc.contributor.author | Antil, Harbir | en |
dc.contributor.author | Warma, Mahamadi | en |
dc.date.accessioned | 2020-06-19T04:18:12Z | - |
dc.date.available | 2020-06-19T04:18:12Z | - |
dc.date.issued | 2018-09 | - |
dc.identifier.issn | 1880-2818 | - |
dc.identifier.uri | http://hdl.handle.net/2433/251624 | - |
dc.description.abstract | In [.r5] we studied optimal control problems with regional fractional p-Laplace equation, of order sin(0, 1) and pin[2, infty), as constraints over a bounded open set with Lipschitz continuous boundary. The control, which fulfills the pointwise box constraints, is given by the coefficient of the regional fractional p-Laplace operator. The purpose of this note is to provide a roadmap on how to apply the results of [5] to the fractional p-Laplace case. The existence and uniqueness of solutions to the state equation and existence of solutions to the optimal control problem follow using similar arguments as in [5]. We prove that the fractional p-Laplacian approaches the standard p-Laplacian as s approaches 1. In this sense, the fractional p-Laplacian can be considered degenerate like the standard p-Laplacian. The remaining steps' are similar to the regional fractional p-Laplacian case, i.e., introduce an auxiliary state equation and the corresponding control problem and then conclude with the convergence of regularized solutions. | en |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | 京都大学数理解析研究所 | ja |
dc.publisher.alternative | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.subject | 35R11 | en |
dc.subject | 49J20 | en |
dc.subject | 49J45 | en |
dc.subject | 93C73 | en |
dc.subject | Fractional $p$-Laplace operator | en |
dc.subject | regional fractional $p$-Laplace operator | en |
dc.subject | non-constant coefficient | en |
dc.subject | quasi-linear nonlocal elliptic boundary value problems | en |
dc.subject | optimal control | en |
dc.subject.ndc | 410 | - |
dc.title | OPTIMAL CONTROL OF THE COEFFICIENT FOR FRACTIONAL $P$-LAPLACE EQUATION : APPROXIMATION AND CONVERGENCE (Theory of Evolution Equation and Mathematical Analysis of Nonlinear Phenomena) | en |
dc.type | departmental bulletin paper | - |
dc.type.niitype | Departmental Bulletin Paper | - |
dc.identifier.ncid | AN00061013 | - |
dc.identifier.jtitle | 数理解析研究所講究録 | ja |
dc.identifier.volume | 2090 | - |
dc.identifier.spage | 102 | - |
dc.identifier.epage | 116 | - |
dc.textversion | publisher | - |
dc.sortkey | 08 | - |
dc.address | Department of Mathematical Sciences, George Mason University | en |
dc.address | University of Puerto Rico (Rio Piedras Campus), College of Natural Sciences, Department of Mathematics | en |
dcterms.accessRights | open access | - |
dc.identifier.jtitle-alternative | RIMS Kokyuroku | en |
出現コレクション: | 2090 発展方程式の理論と非線形現象の数学解析 |
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