Regularity for entropy solutions of degenerate parabolic equations with L^m data

In this paper, we study the regularity results for entropy solutions of a class of parabolic nonlinear parabolic equations with degenerate coercivity, when  the right-hand side is in $L^{m}$ with $m>1$.

regularity
entropy solutions
degenerate coercivity
L^m data
  1. Li F.  Regularity for entropy solution of a class of parabolic equations with irregular data.  Commentationes Mathematicae Universitatis Carolinae.  48 (1), 69–82 (2007).
  2. Prignet A.  Existence and uniqueness of "entropic" solutions of parabolic problems with $L^{1}$ data.  Nonlinear Analysis: Theory, Methods & Applications.  28 (12), 1943–1954 (1997).
  3. Segura de León S, Toledo J.  Regularity for entropy solutions of parabolic $p$-Laplacian equations.  Publicacions Matemàtiques.  43 (2), 665–683 (1999).
  4. Blanchard D., Murat F.  Renormalised solutions of nonlinear parabolic problems with $L^{1}$ data: existence and uniqueness.  Proceedings of the Royal Society of Edinburgh. Section A: Mathematics.  127 (6), 1137–1152 (1997).
  5. Li F.  Existence and regularity results for some parabolic equations with degenerate coercivity.  Annales Academiæ Scientiarum Fennicæ Mathematica.  37, 605–633 (2012).
  6. Mokhtari F., Khelifi H.  Regularity results for degenerate parabolic equations with $L^{m}$ data.  Complex Variables and Elliptic Equations. 1–15 (2022).
  7. Bénilan P. H., Boccardo L., Gallouët T., Gariepy R, Pierre M, Vazquez J. L.  An $L^{1}$-theory of existence and uniqueness of solutions of nonlinear elliptic equations.  Annali della Scuola Normale Superiore di Pisa – Classe di Scienze, Serie 4.  22 (2), 241–273 (1995).
  8. Boccardo L, Dall'Aglio A, Orsina A.  Existence and regularity results for some elliptic equations with degenerate coercivity.  Atti Del Seminario Matematico E Fisico Universita Di Modena.  46, 51–81 (1998).
  9. Bénilan P. H, Brezis H, Crandall M. G.  A semilinear equation in $L^1 (\mathbb {R}^N)$.  Annali della Scuola Normale Superiore di Pisa – Classe di Scienze, Serie 4.  2 (4), 523–555 (1975).
  10. Lions J. L.  Quelques méthodes de résolution des problèmes aux limites nonlinéaires.  Dunod, Paris (1969).
  11. Simon J.  Compact sets in the space $L^{p}(0,T;B)$.  Annali di Matematica Pura ed Applicata.  146, 65–96 (1987).
  12. Porretta A.  Exestence results for nonlinear parabolic equations via strong convergence of truncations.  Annali di Matematica Pura ed Applicata.  177, 143–172 (1999).
  13. Di Benedetto E.  Degenerate parabolic equations. Springer–Verlag, New York (1993).