Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains

2024/07/29 by Mihalis Mourgoglou, Xavier Tolsa, Mourgoglou, Mihalis +1 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2407.20385

Abstract

Let Ω⊂ ℝⁿ⁺¹ be a bounded chord-arc domain, let \mathcal L=-\rm div A∇ be an elliptic operator in Ω associated with a matrix A having Dini mean oscillation coefficients, and let 1p in Ω, ∂ Ω supports a weak p-Poincaré inequality, and Ω has very big pieces of superdomains for which the Neumann problem for \mathcal L is solvable uniformly in L^q, then the Neumann problem for \mathcal L is solvable in L^p in Ω.

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• Equivalent Characterizations and Their Applications of Solvability of L^p Poisson--Robin(-Regularity) Problems on Rough Domains
• Boundary Value Problems in graph Lipschitz domains in the plane with A_∞-measures on the boundary

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