Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Loher, Amélie"'
We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded Fisher information for positive times. This solution is therefore a g
Externí odkaz:
http://arxiv.org/abs/2410.10765
Autor:
Loher, Amélie
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 Strong Harna
Externí odkaz:
http://arxiv.org/abs/2409.02903
Autor:
Loher, Amélie
We derive the Strong Harnack inequality for a class of hypoelliptic integro-differential equations in divergence form. The proof is based on a priori estimates, and as such extends the first non-stochastic approach of the non-local parabolic Strong H
Externí odkaz:
http://arxiv.org/abs/2404.05612
Autor:
Anceschi, Francesca, Dietert, Helge, Guerand, Jessica, Loher, Amélie, Mouhot, Clément, Rebucci, Annalaura
We propose a systematic elementary approach based on trajectories to prove Poincar\'e inequalities for hypoelliptic equations with an arbitrary number of H\"ormander commutators, both in the local and in the non-local case. Our method generalises and
Externí odkaz:
http://arxiv.org/abs/2401.12194
We consider the homogeneous Landau equation in $\mathbb{R}^3$ with Coulomb potential and initial data in polynomially weighted $L^{3/2}$. We show that there exists a smooth solution that is bounded for all positive times. The proof is based on short-
Externí odkaz:
http://arxiv.org/abs/2401.06939
Autor:
Golding, William, Loher, Amélie
We consider the homogeneous Landau equation with Coulomb potential and general initial data $f_{in} \in L^p$, where $p$ is arbitrarily close to $3/2$. We show the local-in-time existence and uniqueness of smooth solutions for such initial data. The c
Externí odkaz:
http://arxiv.org/abs/2308.10288
Autor:
Loher, Amélie
We derive Schauder estimates using ideas from Campanato's approach for a general class of local hypoelliptic operators and non-local kinetic equations. The method covers equations in divergence and non-divergence form. In particular our results are a
Externí odkaz:
http://arxiv.org/abs/2305.00463
We consider the Landau equation with Coulomb potential in the spatially homogeneous case. We show short time propagation of smallness in $L^p$ norms for $p>3/2$ and instantaneous regularization in Sobolev spaces. This yields new short time quantitati
Externí odkaz:
http://arxiv.org/abs/2303.02281
Autor:
Loher, Amélie
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. This permi
Externí odkaz:
http://arxiv.org/abs/2203.16137
