On the First Eigenvalue of the Degenerate p-Laplace Operator in Non-Convex Domains

2017/07/27 by Gol'dshtein, V., Pchelintsev, V., Ukhlov, A. · 1 citation
#30C65 #35P15 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.08867

Abstract

In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, p>2, in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimates constants of Poincaré-Sobolev inequalities and as an application to derive lower estimates of the first non-trivial eigenvalues for the Alhfors domains (i.e. to quasidiscs). This class of domains includes some snowflakes type domains with fractal boundaries.

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• Conformal composition operators with applications to Dirichlet eigenvalues

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