A Reilly inequality for the first Steklov eigenvalue
| Autor: | Saïd Ilias, Ola Makhoul |
|---|---|
| Přispěvatelé: | Ilias, Said, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Université de Tours-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2011 |
| Předmět: |
Reilly inequality
Steklov Boundary (topology) 01 natural sciences Upper and lower bounds r-th mean curvature [MATH.MATH-SP] Mathematics [math]/Spectral Theory [math.SP] First eigenvalue 0101 mathematics Eigenvalues and eigenvectors Mathematics Hsiung–Minkowski formulas Euclidean space 010102 general mathematics Mathematical analysis Mathematics::Spectral Theory Submanifold 010101 applied mathematics Computational Theory and Mathematics Hsiung-Minkowski formulas Mathematics::Differential Geometry Geometry and Topology Laplacian MCS 35P15 35J25 58J30 58J50 Laplace operator Analysis [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] $r$-th mean curvature |
| Zdroj: | Differential Geometry and its Applications. 29:699-708 |
| ISSN: | 0926-2245 |
| Popis: | C'est une partie de la thèse d'Ola Makhoul soutenue en juin 2010, et c'est à paraître,; Let $M$ be a compact submanifold with boundary immersed in a Euclidean space or a Sphere. In this paper, we derive an upper bound for the first non zero eigenvalue $p_1$ of Steklov problem on $M$ in terms of the $r$-th mean curvatures of its boundary $\partial M$. In the Euclidean case, the obtained upper bound is sharp. |
| Databáze: | OpenAIRE |
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