Regularity for entropy solutions of a class of parabolic equations with irregular data

Fengquan Li

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 69-82
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Li, Fengquan. "Regularity for entropy solutions of a class of parabolic equations with irregular data." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 69-82. <http://eudml.org/doc/250197>.

@article{Li2007,
abstract = {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.},
author = {Li, Fengquan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regularity; entropy solutions; parabolic equations; irregular data; regularity; entropy solutions; parabolic equations; irregular data},
language = {eng},
number = {1},
pages = {69-82},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Regularity for entropy solutions of a class of parabolic equations with irregular data},
url = {http://eudml.org/doc/250197},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Li, Fengquan
TI - Regularity for entropy solutions of a class of parabolic equations with irregular data
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 69
EP - 82
AB - 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.
LA - eng
KW - regularity; entropy solutions; parabolic equations; irregular data; regularity; entropy solutions; parabolic equations; irregular data
UR - http://eudml.org/doc/250197
ER -

References

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  8. Porretta A., Regularity for entropy solutions of a class of parabolic equations with nonregular initial datum, Dynam. Systems Appl. 7 (1998), 53-71. (1998) MR1612029
  9. Segura de León S., Estimates for solutions of nonlinear parabolic equations, Boll. Un. Mat. Ital. B (7) 11 (1997), 987-996. (1997) MR1491739
  10. Segura de León S., Toledo J., Regularity for entropy solutions of parabolic P-Laplacian equations, Publ. Mat. 43 (1999), 665-683. (1999) MR1744624
  11. Boccardo L., Gallouët T., Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal. 87 (1989), 149-169. (1989) MR1025884
  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. (1981) MR0635759
  13. Di Benedetto E., Degenerate Parabolic Equations, Springer, New York, 1993. 
  14. Ziemer W.P., Weakly Differentiable Functions, Springer, New York, 1989. Zbl0692.46022MR1014685

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