Regularity for a class of quasilinear degenerate parabolic equations in the Heisenberg group [PDF]
, 2020 We extend to the parabolic setting some of the ideas originated with Xiao Zhong's proof in \cite{Zhong} of the H\"older regularity of $p-$harmonic functions in the Heisenberg group $\Hn$. Given a number $p\ge 2$, in this paper we establish the $C^{\infty}
L. Capogna, G. Citti, N. Garofalo
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Nonlinear degenerate parabolic equations with irregular initial data [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 2021 Existence and regularity results for a class of degenerate nonlinear parabolic equations are proved for irregular initial data like the Dirac mass. Indeed the diffusion operator may degenerate as the solution diverges and may depend on space and time ...
Maria Michaela Porzio
doaj
Direct and inverse source problems for degenerate parabolic equations
Journal of Inverse and Ill-Posed Problems, 2020 Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied ...
M.S Hussein +3 more
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The structure of the singular set in the thin obstacle problem for degenerate parabolic equations [PDF]
Calculus of Variations and Partial Differential Equations, 2019 We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight |y|a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage ...
Agnid Banerjee +3 more
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Communications in Analysis and Mechanics, 2023 In this article, we investigate the initial-boundary value problem for a class of finitely degenerate semilinear parabolic equations with singular potential term.
Huiyang Xu
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Wellposedness of a nonlocal nonlinear diffusion equation of image processing [PDF]
, 2016 Existence and uniqueness are established for a degenerate regularization of the well-known Perona-Malik equation proposed by the first author for non-smooth initial data.
Guidotti, Patrick, Shao, Yuanzhen
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Convergence of Inverse Volatility Problem Based on Degenerate Parabolic Equation
Mathematics, 2022 Based on the theoretical framework of the Black–Scholes model, the convergence of the inverse volatility problem based on the degenerate parabolic equation is studied.
Yilihamujiang Yimamu, Zuicha Deng
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Regularization of outflow problems in unsaturated porous media with dry regions [PDF]
, 2007 We study a porous medium with saturated, unsaturated, and dry regions, described by Richards' equation for the saturation s and the pressure p. Due to a degenerate permeability coefficient k(x,s) and a degenerate capillary pressure function pc(x,s), the ...
Schweizer, Ben
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Carleman inequality for a class of super strong degenerate parabolic operators and applications
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can not be removed
Bruno Sérgio Araújo +2 more
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Second order mean field games with degenerate diffusion and local coupling [PDF]
, 2014 We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility ...
Cardaliaguet, Pierre +3 more
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