29 citations · 116 across the 9 of their papers we have counts for
11 papers
Entropy dissipation estimates for the Boltzmann equation without cut-off
Jamil Chaker, Luis Silvestre
We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted -Norm. The estimate holds for a wide range of potentials including so…
Harnack inequality for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness a…
Regularity for nonlocal problems with non-standard growth
Jamil Chaker, Minhyun Kim, Marvin Weidner
We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of -type and for weak solutions to a related class of nonlocal equ…
Local regularity for nonlocal equations with variable exponents
Jamil Chaker, Minhyun Kim
In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrang…
The concentration-compactness principle for the nonlocal anisotropic -Laplacian of mixed order
Jamil Chaker, Minhyun Kim, Marvin Weidner
In this paper, we study the existence of minimizers of the Sobolev quotient for a class of nonlocal operators with an orthotropic structure having different exponents of integrabil…
Regularity estimates for fractional orthotropic -Laplacians of mixed order
Jamil Chaker, Minhyun Kim
We study robust regularity estimates for a class of nonlinear integro-differential operators with anisotropic and singular kernels. In this paper, we prove a Sobolev-type inequalit…
Parabolic problems for direction-dependent local-nonlocal operators
Jamil Chaker, Moritz Kassmann, Marvin Weidner
We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting co…
Coercivity estimates for integro-differential operators
Jamil Chaker, Luis Silvestre
We provide a general condition on the kernel of an integro-differential operator so that its associated quadratic form satisfies a coercivity estimate with respect to the -sem…
Nonlocal operators with singular anisotropic kernels
Jamil Chaker, Moritz Kassmann
We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves lik…
The martingale problem for a class of nonlocal operators of diagonal type
Jamil Chaker
We consider systems of stochastic differential equations of the form \[ \d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for with continuous, bounded and non-degener…
Regularity of solutions to anisotropic nonlocal equations
Jamil Chaker
We study harmonic functions associated to systems of stochastic differential equations of the form , , w…