Jump formulas for singular integrals and layer potentials on rectifiable sets

DOI10.1090/proc/15199zbMath1446.42021arXiv1811.07837OpenAlexW3032923809MaRDI QIDQ5119230

Xavier Tolsa

Publication date: 3 September 2020

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

Full work available at URL: https://arxiv.org/abs/1811.07837

zbMATH Keywords

double layer potentialCalderón-Zygmund techniques

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Length, area, volume, other geometric measure theory (28A75)

Related Items (5)

Energy minimisers of perturbed dislocation energies ⋮ Unique Continuation at the Boundary for Harmonic Functions in C¹ Domains and Lipschitz Domains with Small Constant ⋮ Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant ⋮ Second order elliptic equations and Hodge-Dirac operators ⋮ Explicit minimizers of some non-local anisotropic energies: a short proof

Cites Work

• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• Variation for singular integrals on Lipschitz graphs: 𝐿^{𝑝} and endpoint estimates
• Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
• Existence and Weak-Type Inequalities for Cauchy Integrals of General Measures on Rectifiable Curves and Sets
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