170 citations · 1.4k across the 61 of their papers we have counts for
8 papers · 1 filter
Perturbations of elliptic operators in 1-sided chord-arc domains. Part II: Non-symmetric operators and Carleson measure estimates
Juan Cavero, Steve Hofmann, José María Martell +1
We generalize to the setting of 1-sided chord-arc domains, that is, to domains satisfying the interior Corkscrew and Harnack Chain conditions (these are respectively scale-invarian…
The regularity problem for uniformly elliptic operators in weighted spaces
Li Chen, José María Martell, Cruz Prisuelos-Arribas
This paper studies the regularity problem for block uniformly elliptic operators in divergence form with complex bounded measurable coefficients. We consider the case where the bou…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part II: The large constant case
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper, along with its companion [Hofmann, Martell, Mayboroda, Toro, Zhao, arXiv:1710.06157], establishes the correspondence between the properties of the solutions of a…
Harmonic measure and quantitative connectivity: geometric characterization of the -solvability of the Dirichlet problem
Jonas Azzam, Steve Hofmann, José María Martell +2
It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak- property) of harmonic measure with respect to surface measure, on the b…
Transference of scale-invariant estimates from Lipschitz to Non-tangentially accessible to Uniformly rectifiable domains
Steve Hofmann, José María Martell, Svitlana Mayboroda
In relatively nice geometric settings, in particular, on Lipschitz domains, absolute continuity of elliptic measure with respect to the surface measure is equivalent to Carleson me…
Fatou-Type Theorems and Boundary Value Problems for Elliptic Systems in the Upper Half-Space
José María Martell, Dorina Mitrea, Irina Mitrea +1
We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-spa…
End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
Kangwei Li, José María Martell, Henri Martikainen +2
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so…
Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition
Murat Akman, Steve Hofmann, José María Martell +1
Let , , be a 1-sided non-tangentially accessible domain (aka uniform domain), i.e., a set which satisfies the interior Corkscrew and Harnack chain…