Strongly elliptic linear operators without coercive quadratic forms. I: Constant coefficient operators and forms

DOI10.4171/JEMS/485zbMath1323.35026OpenAlexW2081843603MaRDI QIDQ479522

Gregory C. Verchota

Publication date: 5 December 2014

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/485

zbMATH Keywords

Neumann problemsum of squaresKorn inequalitynull formLax-Milgram theoremindefinite formLegendre-Hadamard systemRellich identity

Mathematics Subject Classification ID

Quadratic and bilinear forms, inner products (15A63) Higher-order elliptic equations (35J30) Variational methods for higher-order elliptic equations (35J35)

Cites Work

• Analyticity of layer potentials and \(L^{2}\) solvability of boundary value problems for divergence form elliptic equations with complex \(L^{\infty }\) coefficients
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Vector potential theory on nonsmooth domains in \(\mathbb{R}^ 3\) and applications to electromagnetic scattering
• Transmission problems and boundary operator algebras
• The method of layer potentials in electromagnetic scattering theory on nonsmooth domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• The coerciveness problem for integro-differential forms
• Layer potential methods for elliptic homogenization problems
• The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders
• Mixed boundary value problems for the Stokes system
• Spectral theory and iterative methods for the Maxwell system in nonsmooth domains
• The Neumann problem on Lipschitz domains
• On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries
• Oblique and Normal Transmission Problems for Dirac Operators with Strongly Lipschitz Interfaces
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