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2090-08.pdf | 12.93 MB | Adobe PDF | 見る/開く |
タイトル: | OPTIMAL CONTROL OF THE COEFFICIENT FOR FRACTIONAL $P$-LAPLACE EQUATION : APPROXIMATION AND CONVERGENCE (Theory of Evolution Equation and Mathematical Analysis of Nonlinear Phenomena) |
著者: | Antil, Harbir Warma, Mahamadi |
キーワード: | 35R11 49J20 49J45 93C73 Fractional $p$-Laplace operator regional fractional $p$-Laplace operator non-constant coefficient quasi-linear nonlocal elliptic boundary value problems optimal control |
発行日: | Sep-2018 |
出版者: | 京都大学数理解析研究所 |
誌名: | 数理解析研究所講究録 |
巻: | 2090 |
開始ページ: | 102 |
終了ページ: | 116 |
抄録: | 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. |
URI: | http://hdl.handle.net/2433/251624 |
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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