55 research outputs found
Analysis of anisotropic nonlocal operators and jump processes
No full textChaker J. Analysis of anisotropic nonlocal operators and jump processes. Bielefeld: Universität Bielefeld; 2017
Regularity of solutions to anisotropic nonlocal equations
No full textChaker J. Regularity of solutions to anisotropic nonlocal equations. Mathematische Zeitschrift. 2020;296:1135–1155.We study harmonic functions associated to systems of stochastic differential equations of the form dXi t = Ai1( Xt-)dZ1 t + center dot center dot center dot + Aid (Xt-)dZd t, i. {1,..., d}, where Z j t are independent one-dimensional symmetric stable processes of order aj. (0, 2), j. {1,..., d}. In this article we prove Holder regularity of bounded harmonic functions with respect to solutions to such systems
Regularity estimates for fractional orthotropic p-Laplacians of mixed order
No full textChaker J, Ki M. Regularity estimates for fractional orthotropic p-Laplacians of mixed order. Advances in Nonlinear Analysis . 2022;11(1):1307-1331.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 inequality, a weak Harnack inequality, and a local Holder estimate
Entropy dissipation estimates for the Boltzmann equation without cut-off
No full textChaker J, Silvestre L. Entropy dissipation estimates for the Boltzmann equation without cut-off . Kinetic and Related Models. 2023.We prove the the entropy production of the Boltzmann equation, in the non cutoff regime, is bounded from below by a weighted Lp norm of the solution. The estimate holds for a wide range of potentials including soft po-tentials as well as very soft potentials. We discuss applications of this estimate for weak solutions of the Boltzmann equation. In particular, we obtain that weak solutions must be belong to the space L1([0, T], Lpq(Rd)) for some precise exponents p and q
Local regularity for nonlocal equations with variable exponents
No full textChaker J, Ki M. Local regularity for nonlocal equations with variable exponents. Mathematische Nachrichten . 2023;296(9):27 Seiten.In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler-Lagrange equations. We show that weak solutions are locally bounded when the variable exponent p is only assumed to be continuous and bounded. Furthermore, we prove that bounded weak solutions are locally Holder continuous under some additional assumptions on p. On the one hand, the class of admissible exponents is assumed to satisfy a log-Holder-type condition inside the domain, which is essential even in the case of local equations. On the other hand, since we are concerned with nonlocal problems, we need an additional assumption on p outside the domain
Harnack inequality for nonlocal problems with non-standard growth
No full textChaker J, Ki M, Weidner M. Harnack inequality for nonlocal problems with non-standard growth. Mathematische Annalen . 2022;386:533–550 .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 and a weak Harnack inequality for functions in a corresponding De Giorgi class. This paper builds upon a recent work on regularity estimates for such nonlocal problems by the same authors
-Laplacian of mixed order
No full textChaker J, Ki M, Weidner M. The concentration-compactness principle for the nonlocal anisotropic p-Laplacian of mixed order. Nonlinear Analysis : Theory, Methods & Applications . 2023;232: 113254.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 integrability and different orders of differentiability. Our method is based on the concentration-compactness principle which we extend to this class of operators. One consequence of our main result is the existence of a nontrivial nonnegative solution to the corresponding critical problem.& COPY; 2023 Elsevier Ltd. All rights reserved
Nonlocal operators with singular anisotropic kernels
No full textChaker J, Kaßmann M. Nonlocal operators with singular anisotropic kernels. Communications in Partial Differential Equations . 2019;45(1):1-31.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 like a stable process in each direction but with a different index of stability. Its generator is the sum of one-dimensional fractional Laplace operators with different orders of differentiability. We study such operators in the general framework of bounded measurable coefficients. We prove a weak Harnack inequality and Holder regularity results for solutions to corresponding integro-differential equations
Robust Hölder Estimates for Parabolic Nonlocal Operators
No full textChaker J, Kaßmann M, Weidner M. Robust Hölder Estimates for Parabolic Nonlocal Operators. arXiv:1912.09919. 2019.In this work we study parabolic equations determined by nonlocal operators in
a general framework of bounded and measurable coefficients. Our emphasis is on
the weak Harnack inequality and H\"older regularity estimates for solutions of
such equations. We allow the underlying jump measures to be singular with a
singularity that depends on the coordinate direction. This approach also allows
to study several classes of non-singular jump measures that have not been dealt
with so far. The main estimates are robust in the sense that the constants can
be chosen independently of the order of differentiability of the operators
AGEMO I - Programme
No full textÉcole thématique Programme « Archéologie du goût en Méditerranée occidentale dans les sociétés phénicienne et punique » 18-21 novembre 2019 Université de Tunis Laboratoire de Recherche Histoires des Économies et des Sociétés Méditerranéennes Voir le diptyque du programme - Voir l'affiche de l'évènement Lundi 18 novembre Matin Ouverture Sidom Habib, Président de l’Université de Tunis. Chaker Jamil, Doyen de la faculté des sciences humaines et sociales de Tunis. Chaouch Nouha, Directrice de ..
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