90 citations · 253 across the 33 of their papers we have counts for
17 papers · 1 filter
Removable singularities for Lipschitz caloric functions in time varying domains
Joan Mateu, Laura Prat, Xavier Tolsa
In this paper we study removable singularities for regular -Lipschitz solutions of the heat equation in time varying domains. We introduce an associated Lipschitz caloric…
Explicit minimisers of some nonlocal anisotropic energies: a short proof
J. Mateu, M. G. Mora, l. Rondi +2
In this paper we consider nonlocal energies defined on probability measures in the plane, given by a convolution interaction term plus a quadratic confinement. The interaction kern…
-bounded singular integrals on a purely unrectifiable set in
Joan Mateu, Laura Prat
We construct an example of a purely unrectifiable measure in for which the singular integrals associated to the kernels $\displaystyle{K(x)=\frac{P_{2k+1}(x)}{|x…
A family of singular integral operators which control the Cauchy transform
Petr Chunaev, Joan Mateu, Xavier Tolsa
We study the behaviour of singular integral operators of convolution type on associated with the parametric kernels $$ k_t(z):=\frac{(\Re z)^{3}}{|z|^{4}}+t\…
Singular integrals unsuitable for the curvature method whose -boundedness still implies rectifiability
Petr Chunaev, Joan Mateu, Xavier Tolsa
The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the -boundedness of certain singular integral operators to the geo…
Flows for non-smooth vector fields with subexponentially integrable divergence
Albert Clop, Renjin Jiang, Joan Mateu +1
In this paper, we study flows associated to Sobolev vector fields with subexponentially integrable divergence. Our approach is based on the transport equation following DiPerna-Lio…