Boundary Value Problems for Second‐Order Elliptic Operators Satisfying a Carleson Condition

2016/06/13 by Martin Dindoš, Jill Pipher, David Rule · 29 citations
Mathematics · #Advanced Harmonic Analysis Research #Boundary value problem #Differential Equations and Boundary Problems #Dirichlet distribution #Dirichlet problem #Divergence (linguistics) #Domain (mathematical analysis) #Elliptic operator #Lipschitz continuity #Lipschitz domain #Mathematical analysis #Mathematics #Neumann boundary condition #Nonlinear Partial Differential Equations #Norm (philosophy) #Operator (biology) #Order (exchange) #Pure mathematics

paper · open access · doi:10.1002/cpa.21649

published in Communications on Pure and Applied Mathematics 70(7), 1316-1365 (Wiley)

openalex publication_date 2016/06/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/08/05

Abstract

Abstract Let Ω be a Lipschitz domain in , and be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in and of the Neumann problem with data for the operator L on Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operator L to be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc.

Citations

• A New Approach to Absolute Continuity of Elliptic Measure, with Applications to Non-symmetric Equations
• Hp spaces of several variables

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