Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations

DOI10.1090/S0002-9947-2012-05606-6zbMath1271.30027MaRDI QIDQ2841357

Irina Mitrea, Qiang Shi, Marius Mitrea, Emilio Marmolejo Olea

Publication date: 25 July 2013

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

zbMATH Keywords

Dirac operatorHelmholtz operatorClifford analysisMaxwell systemboundary layer potentialstransmission boundary value problems

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Functions of hypercomplex variables and generalized variables (30G35) Integral representations of solutions to PDEs (35C15) (H^p)-spaces (42B30) Boundary value problems for linear first-order PDEs (35F15) Boundary value problems for first-order elliptic systems (35J56) Harmonic analysis and PDEs (42B37)

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Cites Work

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• Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains
• Corner singularity for transmission problems in three dimensions
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter
• 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
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Potential techniques for boundary value problems on \(C^1\)-domains
• Estimates of harmonic measure
• Clifford wavelets, singular integrals, and Hardy spaces
• Vector potential theory on nonsmooth domains in \(\mathbb{R}^ 3\) and applications to electromagnetic scattering
• The method of layer potentials in electromagnetic scattering theory on nonsmooth domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Transmission problems and spectral theory for singular integral operators on Lipschitz domains
• Variable coefficient transmission problems and singular integral operators on non-smooth manifolds
• Die natürlichen Randwertaufgaben im Außenraum für Strahlungsfelder beliebiger Dimension und beliebigen Ranges
• Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
• Boundary Value Problems for Parabolic Lame Systems and a Nonstationary Linearized System of Navier-Stokes Equations in Lipschitz Cylinders
• The Method of Layer Potentials for the Heat Equation in Lipschitz Cylinders
• Transmission problems for the vector Helmholtz equation
• On Single Integral Equations for the Transmission Problem of Acoustics
• On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries
• The Conductive Boundary Condition for Maxwell’s Equations
• Cauchy integrals on Lipschitz curves and related operators
• Regularity Properties of Solutions to Transmission Problems
• On recovering obstacles inside inhomogeneities
• Uniqueness for inverse conductivity and transmission problems in the class of lipschitz domains
• On a Transmission Boundary Value Problem for the Time-Harmonic Maxwell Equations without Displacement Currents
• Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle
• TRANSMISSION PROBLEMS FOR THE LAPLACE AND ELASTICITY OPERATORS: REGULARITY AND BOUNDARY INTEGRAL FORMULATION
• Uniqueness in inverse obstacle scattering with conductive boundary condition
• Boundary value problems for Dirac operators and Maxwell's equations in non‐smooth domains
• Higher Dimensional Electromagnetic Scattering Theory on C 1 and Lipschitz Domains
• Differential operators and boundary value problems on hypersurfaces
• Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\"odinger Operators on Bounded Lipschitz Domains
• On Solutions of Maxwell's Equations in an Exterior Region
• Inverse acoustic and electromagnetic scattering theory
• Kapazität von Strahlungsfeldern
• Generalized Dirac operators on nonsmooth manifolds and Maxwell's equations
• Über die Beugung elektromagnetischer Schwingungen an endlichen homogenen Körpern