The parabolic Harnack inequality for nonlocal equations
M Kassmann, M Weidner - arXiv preprint arXiv:2303.05975, 2023 - arxiv.org
We complete the local regularity program for weak solutions to linear parabolic nonlocal
equations with bounded measurable coefficients. Within the variational framework we prove …
equations with bounded measurable coefficients. Within the variational framework we prove …
[HTML][HTML] Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities
M Bonforte, J Endal - Journal of Functional Analysis, 2023 - Elsevier
We establish boundedness estimates for solutions of generalized porous medium equations
of the form∂ t u+(− L)[um]= 0 in RN×(0, T), where m≥ 1 and− L is a linear, symmetric, and …
of the form∂ t u+(− L)[um]= 0 in RN×(0, T), where m≥ 1 and− L is a linear, symmetric, and …
Fundamental solutions to Kolmogorov-Fokker-Planck equations with rough coefficients: existence, uniqueness, upper estimates
We show the existence and uniqueness of fundamental solution operators to Kolmo\-gorov-
Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion …
Fokker-Planck equations with rough (measurable) coefficients and local or integral diffusion …
Potential theory for nonlocal drift-diffusion equations
The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion
equations via pointwise potential estimates. Our analysis requires only minimal assumptions …
equations via pointwise potential estimates. Our analysis requires only minimal assumptions …
H\" older and Harnack estimates for integro-differential operators with kernels of measure
J Chen - arXiv preprint arXiv:2409.20190, 2024 - arxiv.org
We establish H\" older and Harnack estimates for weak solutions of a class of elliptic
nonlocal equations that are modeled on integro-differential operators with kernels of …
nonlocal equations that are modeled on integro-differential operators with kernels of …
Local behaviour of non-local hypoelliptic equations: divergence form
A Loher - arXiv preprint arXiv:2404.05612, 2024 - arxiv.org
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 …
equations in divergence form. The proof is based on a priori estimates, and as such extends …
Time-insensitive nonlocal parabolic Harnack estimates
We establish new Harnack estimates that defy the waiting-time phenomenon for global
solutions to nonlocal parabolic equations. Our technique allows us to consider general …
solutions to nonlocal parabolic equations. Our technique allows us to consider general …