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The Dirichlet Problem for Second Order Elliptic Operators on Unbounded Domains

Wolfgang L. Walter, Rainer Janben, V. S. Besov

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Abstract

Let be a uniformly strong elliptic operator on an open set ω ⊃ Rnwith boundary ∂ω, where neither ωnor ωis assumed to be bounded. In this paper I prove the existence of weak solutions of the Dirichlet-problem in some weighted Sobolev-spaces. The results refine previous results of Maulen and the author [5]. AMS(MOS) 35J20,26A86

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What this paper is about

Let be a uniformly strong elliptic operator on an open set ω ⊃ Rnwith boundary ∂ω, where neither ωnor ωis assumed to be bounded. In this paper I prove the existence of weak solutions of the Dirichlet-problem in some weighted Sobolev-spaces. The results refine previous results of Maulen and the author [5]. AMS(MOS) 35J20,26A86

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Available abstract

Let be a uniformly strong elliptic operator on an open set ω ⊃ Rnwith boundary ∂ω, where neither ωnor ωis assumed to be bounded. In this paper I prove the existence of weak solutions of the Dirichlet-problem in some weighted Sobolev-spaces. The results refine previous results of Maulen and the author [5]. AMS(MOS) 35J20,26A86

Key concepts: Mathematics, Sobolev space, Open set, Bounded function, Dirichlet problem, Order (exchange), Elliptic operator, Pure mathematics

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