On growth monotonicity estimates of the principal Dirichlet-Laplacian\n eigenvalue

2021/12/01 by Valerii Pchelintsev, Pchelintsev, Valerii
Computer Science · Mathematics · #30C65 #35P15 #46E35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2112.00411

openalex publication_date 2021/12/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In the present paper we obtain growth monotonicity estimates of the principal\nDirichlet-Laplacian eigenvalue in bounded non-Lipschitz domains. The proposed\nmethod is based on composition operators generated by quasiconformal mappings\nand their applications to weighted Sobolev inequalities.\n

Citations

• On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains
• Conformal spectral stability for the Dirichlet-Laplace operator

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