Sobolev spaces on non-Lipschitz subsets of \(\mathbb {R}^n\) with application to boundary integral equations on fractal screens

DOI10.1007/s00020-017-2342-5zbMath1373.46024arXiv1607.01994OpenAlexW2476389126MaRDI QIDQ521897

Simon N. Chandler-Wilde, D. P. Hewett, Andrea Moiola

Publication date: 12 April 2017

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.01994

zbMATH Keywords

Sobolev spacesintegral equationsnon-Lipschitz sets

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Linear integral equations (45A05)

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Cites Work

• Hitchhiker's guide to the fractional Sobolev spaces
• An introduction to Sobolev spaces and interpolation spaces
• Boundary integral equations
• The dichotomy between traces on \(d\)-sets \(\Gamma \) in \(\mathbb R^n\) and the density of \(D(\mathbb R^n \setminus \Gamma )\) in function spaces
• Functional analysis, Sobolev spaces and partial differential equations
• Boundary integral equations for screen problems in \({\mathbb{R}}^ 3\)
• On the boundary integral-equations for the crack opening displacement of flat cracks
• The electric field integral equation on Lipschitz screens: definitions and numerical approximation
• On pointwise multipliers for \(F_{p,q}^s (\mathbb{R}^n)\) in case \(\sigma_{p,q}< s< n/p\)
• Perturbation theory for linear operators.
• Function spaces on fractals
• Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
• Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Integral equations on multi-screens
• Degree-independent Sobolev extension on locally uniform domains
• Polar sets and removable singularities of partial differential equations
• A note on properties of the restriction operator on Sobolev spaces
• Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains
• Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering
• Sur la complétion par rapport à une intégrale de Dirichlet
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Distributions and Operators
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• On Regularity of the Boundary in the Theory of Sobolev Spaces
• Vector potentials in three-dimensional non-smooth domains
• On the behavior of the Sierpinski multiband fractal antenna
• Well-Posed PDE and Integral Equation Formulations for Scattering by Fractal Screens
• INTERPOLATION OF HILBERT AND SOBOLEV SPACES: QUANTITATIVE ESTIMATES AND COUNTEREXAMPLES
• On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space
• A connection between 𝛼-capacity and 𝑚-𝑝 polarity
• Some Integral Inequalities with Applications to the Imbedding of Sobolev Spaces Defined Over Irregular Domains
• Approximation in L p by Solutions of Elliptic Partial Differential Equations
• Sobolev Spaces
• Boundary Element Methods
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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