170 citations · 1.4k across the 61 of their papers we have counts for
17 papers · 1 filter
Solvability of the Dirichlet problem for the heat equation implies parabolic uniform rectifiability
Simon Bortz, Steven Hofmann, José María Martell +1
Let be an open set in space-time with boundary . Under minimal and natural background assumptions - namely, that is time-symmetricall…
Elliptic operators in rough sets, and the Dirichlet problem with boundary data in Hölder spaces
Mingming Cao, Pablo Hidalgo-Palencia, José María Martell +2
In this paper we study the Dirichlet problem for real-valued second order divergence form elliptic operators with boundary data in Hölder spaces. Our context is that of open sets $…
A note on Rubio de Francia's extrapolation in tent spaces and applications
José María Martell, Pierre Portal
The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt w…
Solvability of the Dirichlet problem for the heat equation is equivalent to parabolic uniform rectifiability in the case of a parabolic Lipschitz graph
Simon Bortz, Steven Hofmann, José María Martell +1
We prove that if a parabolic Lipschitz (i.e., Lip(1,1/2)) graph domain has the property that its caloric measure is a parabolic weight with respect to surface measure (w…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of w…
Elliptic measures and Square function estimates on 1-sided chord-arc domains
Mingming Cao, José María Martell, Andrea Olivo
In nice environments, such as Lipschitz or chord-arc domains, it is well-known that the solvability of the Dirichlet problem for an elliptic operator in , for some finite ,…
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…
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…
The generalized Hölder and Morrey-Campanato Dirichlet problems for elliptic systems in the upper-half space
Juan José Marín, José María Martell, Marius Mitrea
We prove well-posedness results for the Dirichlet problem in for homogeneous, second order, constant complex coefficient elliptic systems with boundary data in…
Uniform rectifiability and elliptic operators satisfying a Carleson measure condition. Part I: The small constant case
Steve Hofmann, José María Martell, Svitlana Mayboroda +2
The present paper, along with its sequel, establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We…
The BMO-Dirichlet problem for elliptic systems in the upper-half space and quantitative characterizations of VMO
José María Martell, Dorina Mitrea, Irina Mitrea +1
We prove that for any homogeneous, second order, constant complex coefficient elliptic system , the Dirichlet problem in with boundary data in BMO is well-p…
Absolute continuity between the surface measure and harmonic measure implies rectifiability
Steve Hofmann, José Maria Martell, Svitlana Mayboroda +2
In the present paper we prove that for any open connected set , , and any with absolute contin…
On the -Poisson semigroup associated with elliptic systems
José María Martell, Dorina Mitrea, Irina Mitrea +1
We study the infinitesimal generator of the Poisson semigroup in associated with homogeneous, second-order, strongly elliptic systems with constant complex coefficients in th…
Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions
Steve Hofmann, Jose Maria Martell, Svitlana Mayboroda
Let , , be a uniformly rectifiable set of dimension . Then bounded harmonic functions in satisfy Carleson me…
The higher order regularity Dirichlet problem for elliptic systems in the upper-half space
José María Martell, Dorina Mitrea, Irina Mitrea +1
We identify a large class of constant (complex) coefficient, second order elliptic systems for which the Dirichlet problem in the upper-half space with data in -based Sobolev…
The Dirichlet problem for elliptic systems with data in Köthe function spaces
José María Martell, Dorina Mitrea, Irina Mitrea +1
We show that the boundedness of the Hardy-Littlewood maximal operator on a Köthe function space and on its Köthe dual is equivalent to the well-posed…