Related papers: The weak Harnack inequality for the Boltzmann equa…

We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…

This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…

This work is concerned with the generation of decay estimates in the velocity variable for solutions of the space-inhomogeneous Boltzmann equation without cutoff on a bounded spatial domain for hard and moderately soft potentials. We work…

We apply recent results on regularity for general integro-differential equations to derive a priori estimates in H\"older spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in…

In this paper, we establish optimal hypoelliptic estimates for a class of kinetic equations, which are simplified linear models for the spatially inhomogeneous Boltzmann equation without angular cutoff.

We derive $C^\infty$ a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to point-wise bounds on their mass, energy and entropy densities. We also establish decay estimates for large…

We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies H\"older continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate.…

We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ($\gamma +2s > 2$), under the assumption that the mass, energy, and…

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…

For the spatially inhomogeneous, non-cutoff Boltzmann equation posed in the whole space $\mathbb R^3_x$, we establish pointwise lower bounds that appear instantaneously even if the initial data contains vacuum regions. Our lower bounds…

The purpose of this note is to demonstrate the announced result in [Loher, The Strong Harnack inequality for the Boltzmann equation, S\'eminaire Laurent Schwartz proceeding] by filling the gap in the proof sketch. We prove the semi-local…

In this paper, we study the initial value problem of a Boltzmann type equation with a nonlinear degenerate damping. We prove the existence of global weak solutions with large initial data, in three dimensional space. We rely on a variant…

We consider the spatially inhomogeneous non-cutoff Boltzmann equation with hard potentials in the non-perturbative setting. For initial data with polynomial decay in the velocity variable, we establish the local-in-time existence and…

We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L^\infty$ in the case of hard potentials. As a consequence,…

H\"older estimates and Harnack inequalities are studied for fully nonlinear integro-differential equations under some mild assumptions. We allow the kernels of variable order and critically close to 2.

In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in…

The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of \emph{weak measure solutions}, with and without angular cutoff on the…

A uniform approach is introduced to study the existence of measure valued solutions to the homogeneous Boltzmann equation for both hard potential with finite energy, and soft potential with finite or infinite energy, by using Toscani…

We prove that the Harnack inequality fails for nonlocal kinetic equations. Such equations arise as linearized models for the Boltzmann equation without cutoff and are of hypoelliptic type. We provide a counterexample for the simplest…

This paper is concerned with the inelastic Boltzmann equation without angular cutoff. We work in the spatially homogeneous case. We establish the global-in-time existence of measure-valued solutions under the generic hard potential…