The Hodge-Laplacian. Boundary value problems on Riemannian manifolds

DOI10.1515/9783110484380zbMath1357.58001OpenAlexW4245378310MaRDI QIDQ531035

Marius Mitrea, Irina Mitrea, Dorina Mitrea, Michael E. Taylor

Publication date: 2 August 2016

Published in: De Gruyter Studies in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/9783110484380

zbMATH Keywords

Fredholmness\(L^p\)-solvabilityboundary value problems on Riemannian manifoldsde Rham-Hodge formalismharmonic double layerHodge-Laplacianregular SKT domain

Mathematics Subject Classification ID

Boundary value problems for nonlinear higher-order PDEs (35G30) Boundary value problems on manifolds (58J32) Fredholm integral equations (45B05) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items (12)

The BMO-Dirichlet problem for elliptic systems in the upper half-space and quantitative characterizations of VMO ⋮ Sobolev spaces and \(\nabla\)-differential operators on manifolds. I: Basic properties and weighted spaces ⋮ Hilbert complexes: analysis, applications, and discretizations. Abstracts from the workshop held June 19--25, 2022 ⋮ First-Kind Boundary Integral Equations for the Hodge--Helmholtz Operator ⋮ Second order elliptic equations and Hodge-Dirac operators ⋮ Multilayer potentials for higher-order systems in rough domains ⋮ Coupling of symmetric operators and the third Green identity ⋮ Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces ⋮ Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds ⋮ Compactness, or lack thereof, for the harmonic double layer ⋮ Uniform Shapiro-Lopatinski conditions and boundary value problems on manifolds with bounded geometry ⋮ Boundary value problems for the Brinkman system with \(L^\infty\) coefficients in Lipschitz domains on compact Riemannian manifolds. A variational approach

This page was built for publication: The Hodge-Laplacian. Boundary value problems on Riemannian manifolds