On the Hölder continuity of bounded weak solutions of quasi-linear parabolic inequalities

M. Struwe; M. A. Vivaldi

doi:10.1007/bf01766854

On the Hölder continuity of bounded weak solutions of quasi-linear parabolic inequalities

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf01766854 ◽

1985 ◽

Vol 139 (1) ◽

pp. 175-189 ◽

Cited By ~ 7

Author(s):

M. Struwe ◽

M. A. Vivaldi

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Parabolic Inequalities ◽

Bounded Weak Solutions

Local Hölder regularity for a doubly singular PDE

Communications in Contemporary Mathematics ◽

10.1142/s0219199718500542 ◽

2018 ◽

Vol 22 (03) ◽

pp. 1850054

Author(s):

Eurica Henriques

Keyword(s):

Parabolic Equation ◽

Weak Solutions ◽

Iteration Method ◽

Hölder Continuity ◽

Hölder Regularity ◽

Holder Continuity ◽

Singular Parabolic Equation ◽

Local Hölder Continuity ◽

Singular Pde ◽

Bounded Weak Solutions

We establish the local Hölder continuity for the nonnegative bounded weak solutions of a certain doubly singular parabolic equation. The proof involves the method of intrinsic scaling and the parabolic version of De Giorgi’s iteration method.

Hölder continuity of weak solutions of a class of linear equations with boundary degeneracy

Journal of Differential Equations ◽

10.1016/j.jde.2007.03.026 ◽

2007 ◽

Vol 239 (1) ◽

pp. 99-131 ◽

Cited By ~ 7

Author(s):

Chunpeng Wang ◽

Lihe Wang ◽

Jingxue Yin ◽

Shulin Zhou

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Linear Equations ◽

Holder Continuity ◽

Boundary Degeneracy

Hölder continuity of weak solutions to subelliptic equations with rough coefficients

Memoirs of the American Mathematical Society ◽

10.1090/memo/0847 ◽

2006 ◽

Vol 180 (847) ◽

pp. 0-0 ◽

Cited By ~ 6

Author(s):

Eric T. Sawyer ◽

Richard L. Wheeden

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Subelliptic Equations ◽

Rough Coefficients

HÖLDER CONTINUITY OF WEAK SOLUTIONS FOR DEGENERATE QUASILINEAR SUBELLIPTIC SYSTEMS WITH DIFFERENT WEIGHTS

Communications in Contemporary Mathematics ◽

10.1142/s0219199712500113 ◽

2012 ◽

Vol 14 (02) ◽

pp. 1250011

Author(s):

XUEWE CUI ◽

PENGCHENG NIU ◽

YONGZHONG WANG

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Harnack Inequalities

We establish Hölder continuity of weak solutions for degenerate quasilinear subelliptic systems with different weights, with weak Harnack inequalities obtained here and a generalization of Caffarelli's idea.

Local Hölder continuity of weak solutions to a diffusive shallow medium equation

Nonlinear Analysis ◽

10.1016/j.na.2019.03.013 ◽

2019 ◽

Vol 185 ◽

pp. 306-335 ◽

Cited By ~ 3

Author(s):

Thomas Singer ◽

Matias Vestberg

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Medium Equation ◽

Local Hölder Continuity

Estimates in Morrey Spaces and Hölder Continuity for Weak Solutions to Degenerate Elliptic Systems

manuscripta mathematica ◽

10.1007/s00229-011-0498-x ◽

2011 ◽

Vol 138 (3-4) ◽

pp. 419-437 ◽

Cited By ~ 6

Author(s):

Yan Dong ◽

Pengcheng Niu

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Elliptic Systems ◽

Morrey Spaces ◽

Holder Continuity ◽

Degenerate Elliptic

GlobalL∞-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions

Nonlinear Analysis ◽

10.1016/j.na.2017.02.019 ◽

2017 ◽

Vol 156 ◽

pp. 144-166 ◽

Cited By ~ 3

Author(s):

Cholhun Yu ◽

Dukman Ri

Keyword(s):

Weak Solutions ◽

Elliptic Equations ◽

Hölder Continuity ◽

Growth Conditions ◽

Holder Continuity ◽

Nonstandard Growth ◽

Nonstandard Growth Conditions

Local Hölder continuity of weak solutions for an anisotropic elliptic equation

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-012-0160-7 ◽

2012 ◽

Vol 20 (3) ◽

pp. 463-486 ◽

Cited By ~ 1

Author(s):

Agnese Di Castro

Keyword(s):

Elliptic Equation ◽

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Anisotropic Elliptic Equation ◽

Local Hölder Continuity

Harnack’s inequality and Hölder continuity for weak solutions of degenerate quasilinear equations with rough coefficients

Nonlinear Analysis ◽

10.1016/j.na.2015.05.029 ◽

2015 ◽

Vol 126 ◽

pp. 69-114 ◽

Cited By ~ 8

Author(s):

D.D. Monticelli ◽

S. Rodney ◽

R.L. Wheeden

Keyword(s):

Weak Solutions ◽

Hölder Continuity ◽

Holder Continuity ◽

Quasilinear Equations ◽

Harnack’S Inequality ◽

Rough Coefficients ◽

Harnack's Inequality

\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth

Ukrainian Mathematical Bulletin ◽

10.37069/1810-3200-2019-16-3-7 ◽

2019 ◽

Vol 16 (3) ◽

pp. 403-447

Author(s):

Igor Skrypnik ◽

Mykhailo Voitovych

Keyword(s):

Weak Solutions ◽

Parabolic Equations ◽

Hölder Continuity ◽

Growth Conditions ◽

Holder Continuity ◽

Nonstandard Growth ◽

Elliptic And Parabolic Equations ◽

Functional Classes ◽

Nonstandard Growth Conditions ◽

Quasilinear Elliptic

The article provides an application of the generalized De Giorgi functional classes to the proof of the Hölder continuity of weak solutions to quasilinear elliptic and parabolic equations with nonstandard growth conditions.