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Applicable Analysis
An International Journal
Volume 45, 1992 - Issue 1-4
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Original Articles

The double layer potential operator over polyhedral domains i: solvability in weighted sobolev spaces

Pages 117-134 | Published online: 02 May 2007

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Read on this site (3)

S. Dahlke, H. Harbrecht, M. Utzinger & M. Weimar. (2018) Adaptive Wavelet BEM for Boundary Integral Equations: Theory and Numerical Experiments. Numerical Functional Analysis and Optimization 39:2, pages 208-232.
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Irina Mitrea. (2005) Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions. Numerical Functional Analysis and Optimization 26:7-8, pages 851-878.
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Constantin Bacuta, Victor Nistor & LudmilT. Zikatanov. (2005) Improving the Rate of Convergence of High-Order Finite Elements on Polyhedra I: A Priori Estimates. Numerical Functional Analysis and Optimization 26:6, pages 613-639.
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Articles from other publishers (31)

Marta de León-Contreras & Karl-Mikael Perfekt. (2022) The quasi-static plasmonic problem for polyhedra. Mathematische Annalen 387:3-4, pages 1533-1577.
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Simon N. Chandler-Wilde, Raffael Hagger, Karl-Mikael Perfekt & Jani A. Virtanen. (2023) On the spectrum of the double-layer operator on locally-dilation-invariant Lipschitz domains. Numerische Mathematik 153:4, pages 635-699.
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S. N. Chandler-Wilde & E. A. Spence. (2021) Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains. Numerische Mathematik 150:2, pages 299-371.
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Muhammad Hassan & Benjamin Stamm. (2021) An integral equation formulation of the N -body dielectric spheres problem. Part I: numerical analysis . ESAIM: Mathematical Modelling and Numerical Analysis 55, pages S65-S102.
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Karsten Fritzsch. (2019) Full asymptotics and Laurent series of layer potentials for Laplace's equation on the half‐space. Mathematische Nachrichten 292:6, pages 1271-1303.
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Yu Qiao & Hengguang Li. (2018) Double Layer Potentials on Polygons and Pseudodifferential Operators on Lie Groupoids. Integral Equations and Operator Theory 90:2.
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Stephan Dahlke & Markus Weimar. (2015) Besov regularity for operator equations on patchwise smooth manifolds. Foundations of Computational Mathematics 15:6, pages 1533-1569.
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Catarina Carvalho & Yu Qiao. (2012) Layer potentials C*-algebras of domains with conical points. Central European Journal of Mathematics 11:1, pages 27-54.
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Yu Qiao & Victor Nistor. (2012) Single and Double Layer Potentials on Domains with Conical Points I: Straight Cones. Integral Equations and Operator Theory 72:3, pages 419-448.
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Euan A. Spence, Simon N. Chandler‐Wilde, Ivan G. Graham & Valery P. Smyshlyaev. (2011) A new frequency‐uniform coercive boundary integral equation for acoustic scattering. Communications on Pure and Applied Mathematics 64:10, pages 1384-1415.
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Irina Mitrea & Katharine Ott. (2010) Spectral theory and iterative methods for the Maxwell system in nonsmooth domains. Mathematische Nachrichten 283:6, pages 784-804.
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Simon N. Chandler-Wilde & Peter Monk. (2008) Wave-Number-Explicit Bounds in Time-Harmonic Scattering. SIAM Journal on Mathematical Analysis 39:5, pages 1428-1455.
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Irina Mitrea & Warwick Tucker. (2007) Interval analysis techniques for boundary value problems of elasticity in two dimensions. Journal of Differential Equations 233:1, pages 181-198.
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Wolfgang Hackbusch, Boris N. Khoromskij & Stefan Sauter. (2006) Adaptive Galerkin boundary element methods with panel clustering. Numerische Mathematik 105:4, pages 603-631.
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S. N. Chandler‐Wilde & S. Langdon. (2007) A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons. SIAM Journal on Numerical Analysis 45:2, pages 610-640.
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S. Börm, N. Krzebek & S.A. Sauter. (2005) May the singular integrals in BEM be replaced by zero?. Computer Methods in Applied Mechanics and Engineering 194:2-5, pages 383-393.
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Irina Mitrea. (2004) On the Traction Problem for the Lamé System on Curvilinear Polygons. Journal of Integral Equations and Applications 16:2.
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O. Steinbach & W.L. Wendland. (2001) On C. Neumann's Method for Second-Order Elliptic Systems in Domains with Non-smooth Boundaries. Journal of Mathematical Analysis and Applications 262:2, pages 733-748.
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Olaf Hansen. (2001) On the Essential Norm of the Double Layer Potential on Polyhedral Domains and the Stability of the Collocation Method. Journal of Integral Equations and Applications 13:3.
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Olaf Hansen. (2001) The Local Behavior of the Solution of the Radiosity Equation at the Vertices of Polyhedral Domains in $\rz^3$. SIAM Journal on Mathematical Analysis 33:3, pages 718-750.
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Irina Mitrea. (1999) Spectral radius properties for layer potentials associated with the elastostatics and hydrostatics equations in nonsmooth domains. The Journal of Fourier Analysis and Applications 5:4, pages 385-408.
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Lothar Jentsch & David Natroshvili. (1999) Non-local approach in mathematical problems of fluid-structure interaction. Mathematical Methods in the Applied Sciences 22:1, pages 13-42.
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Johannes Elschner. 1999. The Maz’ya Anniversary Collection. The Maz’ya Anniversary Collection 35 52 .
Gershon Kresin. 1999. The Maz’ya Anniversary Collection. The Maz’ya Anniversary Collection 249 306 .
Stefan A. Sauter. 1998. Wave Propagation in Complex Media. Wave Propagation in Complex Media 199 224 .
Norbert Heubr & Ernst P. Stephan. (2006) Boundary Integral Operators in Countably Normed Spaces. Mathematische Nachrichten 191:1, pages 123-151.
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Dagmar Medková. (1997) The third boundary value problem in potential theory for domains with a piecewise smooth boundary. Czechoslovak Mathematical Journal 47:4, pages 651-679.
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Dorina Mitrea, Marius Mitrea & Jill Pipher. (1997) Vector potential theory on nonsmooth domains in R3 and applications to electromagnetic scattering. The Journal of Fourier Analysis and Applications 3:2, pages 131-192.
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Boris N. Khoromskij & Siegfried Prössdorf. (1995) Multilevel preconditioning on the refined interface and optimal boundary solvers for the Laplace equation. Advances in Computational Mathematics 4:1, pages 331-355.
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Gershon I. Kresin & Vladimir G. Maz'ya. (2005) The norm and the essential norm of the double layer elastic and hydrodynamic potentials in the space of continuous functions. Mathematical Methods in the Applied Sciences 18:14, pages 1095-1131.
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Dirk Mirschinka. (2005) The double layer potential method for a boundary transmission problem for the Laplace operator in an infinite wedge. Mathematical Methods in the Applied Sciences 18:7, pages 515-528.
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