Harnack estimates for weak solutions to a singular parabolic equation

Huashui Zhan

Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (3) : 397 -416.

PDF
Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (3) : 397 -416. DOI: 10.1007/s11401-011-0644-5
Article

Harnack estimates for weak solutions to a singular parabolic equation

Author information +
History +
PDF

Abstract

By an interpolation method, an intrinsic Harnack estimate and some sup-estimates are established for nonnegative solutions to a general singular parabolic equation.

Keywords

Harnack estimate / Interpolation method / Nonnegative solution / Singular parabolic equation

Cite this article

Download citation ▾
Huashui Zhan. Harnack estimates for weak solutions to a singular parabolic equation. Chinese Annals of Mathematics, Series B, 2011, 32(3): 397-416 DOI:10.1007/s11401-011-0644-5

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Hadamard J.. Extension á l’équation de la chaleur d’un théoréme de A. Harnack. Rend. Circ. Mat. Palermo., 1954, 23: 337-346

[2]

Pini B.. Sulla soluzione generalizzata diWinener per il primo problema di valori al contorno nel parabolico. Rend. Sem. Math. Padova., 1954, 23: 422-434

[3]

Moser J.. A Harnack inequality foe parabolic differential equations. Comm. Pure Appl. Math., 1964, 17: 101-134

[4]

Aronson D. G., Serrinm J.. Local behavior of solutions of quasilinear parabolic equations. Arch. Rational Mech. Anal., 1967, 25: 81-123

[5]

Trudinger N. S.. Pointwise estimates and quasilinear parabolic equations. Comm. Pure. Appl. Math., 1968, 21: 205-266

[6]

Ladyzenskaja, O. A., Solonnikov, V. A. and Uralśtzeva, N. N., Linear and quasilinear equations of parabolic type, Transl. Math. Mono., 23, A. M. S., Providence, RI, 1968.

[7]

Dibenedetto E.. Intrinsic Harnack type inequalities foe solutions of certain degenerate parabolic equations. Arch. Rational Mech. Anal., 1988, 100: 129-147

[8]

Dibenedetto E., Kwong Y. C.. Harnack estimates and extinction profile for weak solutions of certain singular parabolic equations. Trans. Amer. Math. Soc., 1992, 330: 783-811

[9]

Dibenedetto E.. Degenerate Parabolic Equations, 1993, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest: Springer-Verlag

[10]

Zhao J., Xu Z. H.. Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equation. Sci. in China, Ser. A, 1996, 39: 73-684

[11]

Yang S.. Harnack estimates for weak solutions of equations of non-Newtonian polytropic filtration. Chin. Ann. Math., 2001, 22B(1): 63-74

AI Summary AI Mindmap
PDF

165

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/