Hölder estimates for quasilinear doubly degenerate parabolic equations. (English. Russian original) Zbl 0729.35018

J. Sov. Math. 56, No. 2, 2320-2347 (1991); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 171, 70-105 (1989).
See the review in Zbl 0719.35008.


35B45 A priori estimates in context of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K65 Degenerate parabolic equations


Zbl 0719.35008
Full Text: DOI


[1] E. DiBenedetto, ”On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),13, No. 3, 487–535 (1986). · Zbl 0635.35052
[2] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Am. Math. Soc., Providence (1968).
[3] C. Yazhe, ”Hölder estimates for solutions of uniformly degenerate quasilinear parabolic equations,” Chinese Ann. Math. Ser. B,5 (4) 661–678 (1984). · Zbl 0562.35051
[4] E. DiBenedetto and A. Friedman, ”Hölder estimates for nonlinear degenerate parabolic systems,” J. Reine Angew. Math.,357, 1–22 (1985). · Zbl 0549.35061
[5] A. V. Ivanov, ”Estimates of the Hölder constants of generalized solutions of degenerate parabolic equations,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,152, 21–44 (1986). · Zbl 0618.35066
[6] A. V. Ivanov, ”Hölder estimates for quasilinear degenerate second-order parabolic systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., 163, 49–65 (1987). · Zbl 0669.35056
[7] N. N. Ural’tseva, ”Degenerate quasilinear elliptic systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,7, 184–221 (1968).
[8] A. V. Ivanov, ”Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order,” Tr. Mat. Inst. Akad. Nauk SSSR, 160 (1982). · Zbl 0517.35001
[9] A. V. Ivanov, ”The Harnack inequality for the generalized solutions of second-order quasilinear parabolic equations,” Tr. Mat. Inst. Akad. Nauk SSSR,102, 51–84 (1967).
[10] M. Tsutsumi, ”On solutions of some doubly nonlinear degenerate parabolic equations with absorption,” J. Math. Anal. Appl.,132, 187–212 (1988). · Zbl 0681.35047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.