SHARP ESTIMATES FOR THE FIRST p-LAPLACIAN EIGENVALUE AND FOR THE p-TORSIONAL RIGIDITY ON CONVEX SETS WITH HOLES

Paoli Gloria; Piscitelli Gianpaolo; Trani Leonardo

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SHARP ESTIMATES FOR THE FIRST p-LAPLACIAN EIGENVALUE AND FOR THE p-TORSIONAL RIGIDITY ON CONVEX SETS WITH HOLES

机译：对于第一个P-LAPLACIAN特征值的急剧估计和凸起凸起凸起的P扭转刚度

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摘要

We study, in dimension n = 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.

机译：我们在尺寸n> = 2，特征值问题和P-Laplacian的扭转刚度，凸起的孔与孔，外部罗宾边界条件和内部Neumann边界条件。我们证明环形空值最大化第一特征值，并使测量和外部周长固定时最小化扭转刚度。

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来源
《ESAIM》 |2020年第1期|111.1-111.15|共15页
作者
Paoli Gloria; Piscitelli Gianpaolo; Trani Leonardo;
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作者单位

Univ Napoli Federico II Complesso Univ Monte S Angelo Dipartimento Matemat & Applicaz R Caccioppoli Via Cintia I-80126 Naples Italy;

Univ Cassino & Lazio Meridionale Dipartimento Ingn Elettr & Informaz M Scarano Via G Biasio 43 I-03043 Cassino FR Italy;

Univ Napoli Federico II Complesso Univ Monte S Angelo Dipartimento Matemat & Applicaz R Caccioppoli Via Cintia I-80126 Naples Italy;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Nonlinear eigenvalue problems; torsional rigidity; mixed boundary conditions; optimal estimates;

机译：非线性特征值问题;扭转刚度;混合边界条件;最优估计;

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1. Sharp gradient estimate and spectral rigidity for p-Laplacian [J] . Chiung-Jue Anna Sung, Jiaping Wang Mathematical research letters: MRL . 2014,第4期

机译：p-Laplacian的陡峭梯度估计和光谱刚度
2. Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound [J] . Aaron Naber, Daniele Valtorta Mathematische Zeitschrift . 2014,第3a4期

机译：对带有Ricci下界为负的p-Laplacian的第一特征值的敏锐估计
3. Sharp estimate on the first eigenvalue of the p-Laplacian [J] . Valtorta D. Nonlinear Analysis: An International Multidisciplinary Journal . 2012,第13期

机译：对p-Laplacian的第一个特征值的敏锐估计
4. Estimates from below for the first eigenvalue of the p-Laplacian [C] . Nikolai Kutev, Tsviatko Rangelov International Conference on New Trends in the Applications of Differential Equations in Sciences . 2019

机译：从下面估计为p-laplacian的第一个特征值
5. On Asymptotics of Nonlocal p-Laplacian Operators and Related Eigenvalues [D] . LI Feng, 李峰 2019

机译：非局部p-Laplacian算子及其相关特征值的渐近性
6. Plasmonic black metals via radiation absorption by two-dimensional arrays of ultra-sharp convex grooves [O] . Jonas Beermann, René L. Eriksen, Tobias Holmgaard, -1

机译：等离子黑金属通过超锐利凸形凹槽二维阵列的辐射吸收
7. Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes [O] . Gloria Paoli, Gianpaolo Piscitelli, Leonardo Trani 2020

机译：对于第一个P-LAPLACIAN特征值的急剧估计和凸起凸起凸起的P扭转刚度

SHARP ESTIMATES FOR THE FIRST p-LAPLACIAN EIGENVALUE AND FOR THE p-TORSIONAL RIGIDITY ON CONVEX SETS WITH HOLES

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