Sharp estimates on the first Dirichlet eigenvalue of nonlinear elliptic operators via maximum principle
| Autor: | Giuseppina di Blasio, Francesco Della Pietra, Nunzia Gavitone |
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| Přispěvatelé: | DELLA PIETRA, Francesco, DI BLASIO, Giuseppina, Gavitone, Nunzia, Della Pietra, Francesco |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Lambda 01 natural sciences Omega Domain (mathematical analysis) anisotropic operator Maximum principle Dirichlet eigenvalue Mathematics - Analysis of PDEs 35p30 FOS: Mathematics optimal estimate 0101 mathematics Mathematics QA299.6-433 49q10 optimal estimates 010102 general mathematics Function (mathematics) Eigenfunction Mathematics::Spectral Theory anisotropic operators 010101 applied mathematics Elliptic operator 35P30 49Q10 Analysis dirichlet eigenvalues Analysis of PDEs (math.AP) |
| Zdroj: | Advances in Nonlinear Analysis, Vol 9, Iss 1, Pp 278-291 (2018) |
| Popis: | In this paper, we study optimal lower and upper bounds for functionals involving the first Dirichlet eigenvalue λ F ( p , Ω ) {\lambda_{F}(p,\Omega)} of the anisotropic p-Laplacian, 1 < p < + ∞ {1 . Our aim is to enhance, by means of the 𝒫 {\mathcal{P}} -function method, how it is possible to get several sharp estimates for λ F ( p , Ω ) {\lambda_{F}(p,\Omega)} in terms of several geometric quantities associated to the domain. The 𝒫 {\mathcal{P}} -function method is based on a maximum principle for a suitable function involving the eigenfunction and its gradient. |
| Databáze: | OpenAIRE |
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