An extension of a Theorem of V. \vSver'ak to variable exponent spaces

2013/11/26 by Carla Baroncini, Baroncini, Carla, Julián Fernández Bonder +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1311.6757

Abstract

In 1993, V. vSver 'ak proved that if a sequence of uniformly bounded\ndomains \Ω_n\⊂ mathbb R² such that \Ω_n\→ \Ω in the\nsense of the Hausdorff complementary topology, verify that the number of\nconnected components of its complements are bounded, then the solutions of the\nDirichlet problem for the Laplacian with source f\∈ L²( mathbb R²)\nconverges to the solution of the limit domain with same source. In this paper,\nwe extend vSver 'ak result to variable exponent spaces.\n

Citations

• The Wiener test and potential estimates for quasilinear elliptic equations

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