Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations

Tuomo Kuusi

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2008)

  • Volume: 7, Issue: 4, page 673-716
  • ISSN: 0391-173X

Abstract

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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.

How to cite

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Kuusi, Tuomo. "Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.4 (2008): 673-716. <http://eudml.org/doc/272265>.

@article{Kuusi2008,
abstract = {In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.},
author = {Kuusi, Tuomo},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {degenerate -Laplacean; Moser's and Trudinger approach; hot and cold alternatives; Krylov-Safonov covering argument},
language = {eng},
number = {4},
pages = {673-716},
publisher = {Scuola Normale Superiore, Pisa},
title = {Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations},
url = {http://eudml.org/doc/272265},
volume = {7},
year = {2008},
}

TY - JOUR
AU - Kuusi, Tuomo
TI - Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2008
PB - Scuola Normale Superiore, Pisa
VL - 7
IS - 4
SP - 673
EP - 716
AB - In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
LA - eng
KW - degenerate -Laplacean; Moser's and Trudinger approach; hot and cold alternatives; Krylov-Safonov covering argument
UR - http://eudml.org/doc/272265
ER -

References

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