Results 1 to 10 of about 84 (83)

Regularity estimates for fractional orthotropic p-Laplacians of mixed order

Advances in Nonlinear Analysis, 2022
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 Hölder estimate.
Chaker Jamil, Kim Minhyun
doaj   +1 more source

Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations

Boundary Value Problems, 2006
We investigate local and global properties of positive solutions to the fast diffusion equation ut=Δum in the good exponent range (d−2 ...
Juan Luis Vazquez, Matteo Bonforte
doaj   +1 more source

Compactness methods for Hölder estimates of certain degenerate elliptic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2012
In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations,
Fengping Yao, Mijia Lai, Huilian Jia
doaj   +1 more source

Harnack Inequalities and ABP Estimates for Nonlinear Second-Order Elliptic Equations in Unbounded Domains

Abstract and Applied Analysis, 2008
We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary.
M. E. Amendola, L. Rossi, A. Vitolo
doaj   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

On the De Giorgi-Nash-Moser regularity theory for kinetic equations

Bruno Pini Mathematical Analysis Seminar
In this note we review some recent results regarding the De Giorgi-Nash-Moser weak regularity theory for Kolmogorov operators obtained in [10] in collaboration with A. Rebucci.
Francesca Anceschi
doaj   +1 more source

Qualitative properties of solutions to parabolic anisotropic equations, part II — The anisotropic Trudinger's equation

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's equation ut−∑i=1NDiu2−pi|Diu|pi−2Diu=0,u⩾0.$$\begin{equation*} u_t- \sum \limits _{i=1}^N D_i{\left(u^{2-p_i}|D_i u|^{p_i-2} D_i u\right)}=0,\qquad u\geqslant 0.
S. Ciani, E. Henriques, M. O. Savchenko, I. I. Skrypnik   +3 more
wiley   +1 more source

Local boundedness and Harnack inequality for an inverse variational inequality problem with double nonlinear parabolic operator in finance

Journal of Inequalities and Applications
The objective of this paper is to investigate a class of initial boundary value problems for inverse variational inequalities that arise from financial matters.
Jia Li, Zhipeng Tong
doaj   +1 more source

Spreading Speed for a Vector‐Borne Disease System on Non‐Coincident Straight Infinite Cylinders

Studies in Applied Mathematics, Volume 156, Issue 6, June 2026.
ABSTRACT Vector‐borne diseases remain an increasing global public health concern. In this work, we investigate the spreading speed of vector‐borne disease via a four‐component reaction–diffusion system posed on non‐coincident straight infinite cylinders, which stands for an unconventional spatial configuration.
Arnaud Ducrot, Hongliang Li, David Manceau   +2 more
wiley   +1 more source

Quasibounded solutions to the complex Monge–Ampère equation

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract We study the Dirichlet problem for the complex Monge–Ampère operator on B‐regular domains in Cn$\mathbb {C}^n$, allowing boundary data that is singular or unbounded. We extend the concept of pluri‐quasibounded functions on the domain to functions on the boundary, defined by the existence of plurisuperharmonic majorants that dominate their ...
Mårten Nilsson
wiley   +1 more source