Harnack type estimates and Holder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations

Emmanuele DiBenedetto; Ugo Gianazza; Vincenzo Vespri

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Harnack type estimates and Holder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations

机译：某些次临界奇异抛物型偏微分方程非负解的Harnack类型估计和Holder连续性

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摘要

A two-parameter family of Harnack type inequalities for non-negative solutions of a class of singular, quasilinear, homogeneous parabolic equations is established, and it is shown that such estimates imply the Holder continuity of solutions. These classes of singular equations include p-Laplacean type equations in the sub-critical range 1 < p ≤ 2N N+1 and equations of the porous medium type in the sub-critical range 0 < m ≤ (NN2)+

机译：建立了一类奇异，拟线性，齐次抛物方程的非负解的两参数Harnack型不等式族，证明了这种估计意味着解的Holder连续性。这些奇异方程组包括在亚临界范围1 ≤2N N + 1中的p-Laplacean型方程和在亚临界范围0

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《Manuscripta mathematica》 |2010年第2期|共15页
作者
Emmanuele DiBenedetto; Ugo Gianazza; Vincenzo Vespri;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
continuity; equations; solutions;

机译：连续性;方程;解;

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专利

1. Harnack type estimates and Holder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations [J] . Emmanuele DiBenedetto, Ugo Gianazza, Vincenzo Vespri Manuscripta mathematica . 2010,第1a2期

机译：某些次临界奇异抛物型偏微分方程非负解的Harnack类型估计和Holder连续性
2. Harnack estimates for non-negative weak solutions of a class of singular parabolic equations [J] . S. Fornaro, V. Vespri Manuscripta Mathematica . 2013,第1a2期

机译：一类奇异抛物方程的非负弱解的Harnack估计
3. Harnack estimates for non-negative weak solutions of a class of singular parabolic equations [J] . Fornaro S., Vespri V. Manuscripta mathematica . 2013,第1a2期

机译：一类奇异抛物方程的非负弱解的Harnack估计
4. Direct methods for numerical solution of singular integro-differential equations in classical Holder spaces (case γ≠ 0) [C] . Iurie Caraus, Nikos E. Mastorakis WSEAS International Conferences . 2008

机译：经典支架空间中奇异积分微分方程数值解的直接方法（案例γ≠0）
5. A Harnack inequality and Holder continuity for weak solutions to parabolic operators with Hormander vector fields. [D] . Rea, Garrett James. 2010

机译：具有荷曼德矢量场的抛物线算子的弱解的Harnack不等式和Holder连续性。
6. Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions [O] . Fritz John 1976

机译：高维非线性偏微分方程解的延迟奇异性形成。
7. Intrinsic Harnack Inequalities for Quasi–Linear Singular Parabolic Partial Differential Equations [O] . Emmanuele Dibenedetto, Ugo Gianazza, Vincenzo Vespri 2015

机译：拟线性奇异抛物型偏微分方程的本征Harnack不等式

Harnack type estimates and Holder continuity for non-negative solutions to certain sub-critically singular parabolic partial differential equations

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