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Title: Regularity for entropy solutions of a class of parabolic equations with irregular data (English)
Author: Li, Fengquan
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 48
Issue: 1
Year: 2007
Pages: 69-82
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Category: math
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Summary: Using as a main tool the time-regularizing convolution operator introduced by R. Landes, we obtain regularity results for entropy solutions of a class of parabolic equations with irregular data. The results are obtained in a very general setting and include known previous results. (English)
Keyword: regularity
Keyword: entropy solutions
Keyword: parabolic equations
Keyword: irregular data
MSC: 35B65
MSC: 35D10
MSC: 35D99
MSC: 35K20
MSC: 35K55
idZBL: Zbl 1199.35141
idMR: MR2338830
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Date available: 2009-05-05T17:01:23Z
Last updated: 2012-05-01
Stable URL: http://hdl.handle.net/10338.dmlcz/119639
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Reference: [1] Bénilan Ph., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vazquez J.L.: An $L^1$-theory of existence and uniqueness of solutions of non-linear elliptic equations.Ann. Scuola Norm. Sup. Pisa. (2) 22 (1995), 240-273. MR 1354907
Reference: [2] Prignet A.: Existence and uniqueness of ``entropic'' solutions of parabolic problems with $L^1$ data.Nonlinear Anal. 28 12 (1997), 1943-1954. MR 1436364
Reference: [3] Porretta A.: Existence results for nonlinear parabolic equations via strong convergence of truncations.Ann. Mat. Pura Appl. 177 (1999), 143-172. Zbl 0957.35066, MR 1747629
Reference: [4] Porretta A.: Some remarks on the regularity of solutions for a class of elliptic equations with measure data.Houston J. Math. 26 1 (2000), 183-213. Zbl 0974.35032, MR 1814734
Reference: [5] Benilan Ph., Brezis H., Crandall M.G.: A semilinear equation in $L^1(R^N)$.Ann. Scuola Norm. Sup. Pisa 2 (1975), 523-555. MR 0390473
Reference: [6] Boccardo L., Dall'aglio A., Gallouët T., Orsina L.: Nonlinear parabolic equations with measure data.J. Funct. Anal. 147 (1997), 237-258. MR 1453181
Reference: [7] Andreu F., Mazon J.M., Segura de León S., Toledo J.: Existence and uniqueness for a degenerate parabolic equation with $L^1$ data.Trans. Amer. Math. Soc. 351 1 (1999), 285-306. MR 1433108
Reference: [8] Porretta A.: Regularity for entropy solutions of a class of parabolic equations with nonregular initial datum.Dynam. Systems Appl. 7 (1998), 53-71. MR 1612029
Reference: [9] Segura de León S.: Estimates for solutions of nonlinear parabolic equations.Boll. Un. Mat. Ital. B (7) 11 (1997), 987-996. MR 1491739
Reference: [10] Segura de León S., Toledo J.: Regularity for entropy solutions of parabolic P-Laplacian equations.Publ. Mat. 43 (1999), 665-683. MR 1744624
Reference: [11] Boccardo L., Gallouët T.: Nonlinear elliptic and parabolic equations involving measure data.J. Funct. Anal. 87 (1989), 149-169. MR 1025884
Reference: [12] Landes R.: On the existence of weak solutions for quasilinear parabolic boundary value problems.Proc. Royal. Soc. Edinburgh Sect. A 89 (1981), 217-237. MR 0635759
Reference: [13] Di Benedetto E.: Degenerate Parabolic Equations.Springer, New York, 1993.
Reference: [14] Ziemer W.P.: Weakly Differentiable Functions.Springer, New York, 1989. Zbl 0692.46022, MR 1014685
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