From the 1 of 7 linked papers with an AI index.
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7 papers
Solvability of the Neumann problem for elliptic equations in chord-arc domains with very big pieces of good superdomains
Mihalis Mourgoglou, Xavier Tolsa
The paper proves that for a bounded chord-arc domain with Dini‑oscillating coefficients, if the regularity problem is solvable in some L^q (q>p), the boundary satisfies a weak p‑Po…
The Dirichlet problem as the boundary of the Poisson problem: A sharp approximation result
Mihalis Mourgoglou, Bruno Poggi
On a bounded domain , , satisfying the corkscrew condition and with Ahlfors regular boundary, we characterize the dual space to the space ${\bf N}…
Smooth extensions of Sobolev boundary data in corkscrew domains with uniformly rectifiable boundaries
Jonas Azzam, Mihalis Mourgoglou, Michele Villa
Given a corkscrew domain with uniformly rectifiable boundary, we construct a surjective trace map onto the Hajlasz-Sobolev space on the boundary from the space of functions o…
Quantitative differentiability on uniformly rectifiable sets
Jonas Azzam, Mihalis Mourgoglou, Michele Villa
We prove quantitative differentiability estimates for functions defined on uniformly rectifiable subsets of the Euclidean space. More precisely, we show that a Dorronsoro-typ…
Layer potentials for elliptic operators with DMO-type coefficients: big pieces theorem, quantitative rectifiability, and free boundary problems
Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti
For , we consider the operator , where is a uniformly elliptic matrix with variable coefficients, a Radon mea…
Solvability of the Poisson-Dirichlet problem with interior data in -Carleson spaces and its applications to the -regularity problem
Mihalis Mourgoglou, Bruno Poggi, Xavier Tolsa
We prove that the -solvability of the homogeneous Dirichlet problem for an elliptic operator with real and merely bounded coefficients is equ…