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regularity; entropy solutions; parabolic equations; irregular data
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.
[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
[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
[3] Porretta A.: Existence results for nonlinear parabolic equations via strong convergence of truncations. Ann. Mat. Pura Appl. 177 (1999), 143-172. MR 1747629 | Zbl 0957.35066
[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. MR 1814734 | Zbl 0974.35032
[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
[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
[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
[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
[9] Segura de León S.: Estimates for solutions of nonlinear parabolic equations. Boll. Un. Mat. Ital. B (7) 11 (1997), 987-996. MR 1491739
[10] Segura de León S., Toledo J.: Regularity for entropy solutions of parabolic P-Laplacian equations. Publ. Mat. 43 (1999), 665-683. MR 1744624
[11] Boccardo L., Gallouët T.: Nonlinear elliptic and parabolic equations involving measure data. J. Funct. Anal. 87 (1989), 149-169. MR 1025884
[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
[13] Di Benedetto E.: Degenerate Parabolic Equations. Springer, New York, 1993.
[14] Ziemer W.P.: Weakly Differentiable Functions. Springer, New York, 1989. MR 1014685 | Zbl 0692.46022
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