Results 51 to 60 of about 472,112 (168)

Li-Yau type estimation of a semilinear parabolic system along geometric flow

Journal of Inequalities and Applications
This article provides a Li–Yau-type gradient estimate for a semilinear weighted parabolic system of semilinear equations along an abstract geometric flow on a smooth measure space. A Harnack-type inequality on the system is also derived at the end.
Yanlin Li, Sujit Bhattacharyya, Shahroud Azami, Shyamal Kumar Hui   +3 more
doaj   +1 more source

Regularity and separation for Grušin‐type p‐Laplace operators

Mathematische Nachrichten, Volume 298, Issue 5, Page 1727-1757, May 2025.
Abstract We analyze p‐Laplace type operators with degenerate elliptic coefficients. This investigation includes Grušin‐type p‐Laplace operators. We describe a separation phenomenon in elliptic and parabolic p‐Laplace type equations, which provide an illuminating illustration of simple jump discontinuities of the corresponding weak solutions ...
Daniel Hauer, Adam Sikora
wiley   +1 more source

Harnack inequality and no-arbitrage bounds for self-financing portfolios [PDF]

We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant.
Polidoro, Sergio, Pascucci, Andrea, Carciola, Alessandro   +2 more
core  

A subelliptic analogue of Aronson–Serrin’s Harnack inequality [PDF]

, 2013
We show that the Harnack inequality for a class of degenerate parabolic quasilinear PDE associated to a system of Lipschitz continuous Hormander vector fields follows from the basic hypothesis of doubling condition and a weak Poincar\'e ...
Garrett Rea, Rea, Garrett, Luca Capogna, CITTI, GIOVANNA, Capogna, Luca   +4 more
core   +1 more source

The parabolic Harnack inequality for nonlocal equations

Kaßmann M, Weidner M. The parabolic Harnack inequality for nonlocal equations. Duke Mathematical Journal. 2024;173(17):3413-3451.We complete the local regularity program for weak solutions to linear parabolic nonlocal equations with bounded measurable ...
Kaßmann, Moritz ; https://orcid.org/, Weidner, Marvin   +1 more
core   +1 more source

A Harnack inequality for degenerate parabolic equations

, 2006
We prove a Harnack inequality for a degenerate parabolic equation using proper estimates based on a suitable version of the Rayleigh ...
GIANAZZA, UGO PIETRO, VESPRI V.
core   +1 more source

The free boundary for semilinear problems with highly oscillating singular terms

Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.
Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen, Dennis Kriventsov, Henrik Shahgholian   +2 more
wiley   +1 more source

Localization and multiplicity in the homogenization of nonlinear problems

Advances in Nonlinear Analysis, 2019
We propose a method for the localization of solutions for a class of nonlinear problems arising in the homogenization theory. The method combines concepts and results from the linear theory of PDEs, linear periodic homogenization theory, and nonlinear ...
Bunoiu Renata, Precup Radu
doaj   +1 more source

Time‐insensitive nonlocal parabolic Harnack estimates

Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.
Abstract 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 nonlocal operators with bounded measurable coefficients. Moreover, we show that a waiting‐time is required for the nonlocal parabolic Harnack inequality when local solutions ...
Naian Liao, Marvin Weidner
wiley   +1 more source