Hölder continuity of weak solutions to subelliptic equations with rough coefficients

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.

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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

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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.

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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

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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

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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

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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

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\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.

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