Existence and uniqueness for a semilinear elliptic problem on Lipschitz domains in Riemannian manifolds II

DOI10.1090/S0002-9947-02-03210-5zbMath1116.58302WikidataQ115289120 ScholiaQ115289120MaRDI QIDQ4787465

Martin Dindoš

Publication date: 7 January 2003

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Riemannian manifoldsnonlinear equationssemilinear elliptic problemsLipschitz domainsDirichlet boundary problems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Boundary value problems on manifolds (58J32)

Related Items

Poisson-transmission problems for \(L^\infty\)-perturbations of the Stokes system on Lipschitz domains in compact Riemannian manifolds, Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman systems in Lipschitz domains, Quasilinear elliptic inequalities on complete Riemannian manifolds, A novel application of the classical Banach fixed point theorem, Large solutions for Yamabe and similar problems on domains in Riemannian manifolds

Cites Work

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• Curvature and uniformization
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
• Potential techniques for boundary value problems on \(C^1\)-domains
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• Vector potential theory on nonsmooth domains in \(\mathbb{R}^ 3\) and applications to electromagnetic scattering
• Elliptic partial differential equations of second order
• Solvability of Dirichlet problems for semilinear elliptic equations on certain domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
• On the existence of positive solutions for semilinear elliptic equations with singular lower order coefficients and Dirichlet boundary conditions
• Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
• On functions of bounded mean oscillation
• On the Poisson integral for Lipschitz and $C^{1}$-domains
• Potential theory on lipschitz domains in riemannian manifolds: hölder continuous metric tensors
• Global Uniqueness for a Two-Dimensional Semilinear Elliptic Inverse Problem
• Potential theory on Lipschitz domains in Riemannian manifolds: \(L^p\) Hardy, and Hölder space results