On the boundary values of the solutions of linear elliptic equations

DOI10.1017/S0004972700011461zbMath0518.35031MaRDI QIDQ3667271

H. B. Thompson, J. H. Chabrowski

Publication date: 1983

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemSobolev spaceenergy estimateboundary values of the solutionstraces of weak solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Generalized solutions to partial differential equations (35D99)

Related Items (13)

On the Dirichlet problem for a quasi-linear elliptic equation ⋮ The Dirichlet problem in half-space for elliptic equations with unbounded coefficients ⋮ On positive solutions for a class of elliptic boundary value problems ⋮ The Dirichlet problem for Lévy-stable operators with \(L^2\)-data ⋮ On the existence of solutions of the Dirichlet problem for nonlinear elliptic equations ⋮ On the solvability of the Dirichlet problem for nonlinear elliptic equations ⋮ Quasilinear ellipticity and the Dirichlet problem ⋮ Note on the Dirichlet problem with \(L^ 2-\)boundary data ⋮ Some existence theorems for the Dirichlet problem for quasilinear elliptic equations ⋮ On the Dirichlet problem for degenerate elliptic equations ⋮ Dirichlet problem for a linear elliptic equation in unbounded domains with \(L^ 2\)-boundary data ⋮ Remarks on multiplicity results for the Dirichlet problem for nonlinear elliptic equations ⋮ On the Dirichlet problem for a semi-linear elliptic equation with \(L^ 2\)-boundary data

Cites Work

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• On the regularity of solutions of second-order elliptic partial differential equations with an unbounded Dirichlet integral
• On the boundary values of the solutions of elliptic equations
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Linear and quasilinear elliptic equations
• Elliptic Partial Differential Equations of Second Order
• Theorems on Fourier Series and Power Series (II)^†

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