Unique solvability of the Dirichlet problem for the equation $\Delta _p u=0$ in the exterior of a paraboloid

DOI10.1090/S1061-0022-2013-01250-7zbMath1279.35029MaRDI QIDQ2849091

S. V. Poborchii

Publication date: 16 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemunbounded domaindomain with infinite locally-Lipschitz boundarylocally-Lipschitz boundarytraces of functions with gradient in \(L_p\)

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Cites Work

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• Existence and uniqueness of a solution to the Dirichlet problem for a quasilinear equation inside and outside a paraboloid
• Existence and uniqueness of an energy solution to the Dirichlet problem for the Laplace equation in the exterior of a multi-dimensional paraboloid
• Unique solvability of the integral equation for harmonic simple layer potential on the boundary of a domain with a peak
• Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in \(n\) variabili
• Linear and quasilinear elliptic equations

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