Publication Cover
Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 16
123
Views
1
CrossRef citations to date
0
Altmetric
Articles

Some fundamental a priori estimates for weak solutions of the evolution p-Laplacian equation

, &
Pages 2793-2806 | Received 28 Sep 2018, Accepted 14 Feb 2019, Published online: 27 Feb 2019

References

  • Kalashnikov AS. Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations. Russian Math Surveys. 1987;42:169–222. doi: 10.1070/RM1987v042n02ABEH001309
  • Lions JL. Quelques méthodes de résolution des problèmes aux limites non linéaires. Paris: Dunod; 1969.
  • Wu Z, Zhao J, Yin J, et al. Nonlinear diffusion equations. Hong Kong: World Scientific; 2001.
  • Zhao J. Existence and nonexistence of solutions for ut=div(∣∇u∣p−2∇u)+f(∇u,u,x,t). J Math Anal Appl. 1993;172:130–146. doi: 10.1006/jmaa.1993.1012
  • Zhou S. A priori L∞-estimate and existence of solutions for some nonlinear parabolic equations. Nonlinear Anal. 2000;42:887–904. doi: 10.1016/S0362-546X(99)00135-2
  • Chagas JQ, Guidolin PL, Zingano PR. Global solvability results for parabolic equations with p-Laplacian type diffused (accepted). J Math Anal Appl. 2018;458:860–874. doi: 10.1016/j.jmaa.2017.09.040
  • Braz e Silva P, Schütz L, Zingano PR. On some energy inequalities and supnorm estimates for advection-diffusion equations in Rn. Nonlin Anal. 2013;93:90–96. doi: 10.1016/j.na.2013.07.028
  • DiBenedetto E. Degenerate parabolic equations. New York: Springer; 1993.
  • Guidolin PL. Contributions to the theory of the evolution p-Laplacian equation (in Portuguese), Doctorate Thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil, September 2015.
  • Zingano PR, Steinberg SL. On the Hardy-Littlewood theorem for functions of bounded variation. SIAM J Math Anal. 2002;33:1199–1210. doi: 10.1137/S0036141000369307
  • Bianchini S, Colombo M, Crippa G, et al. Optimality of integrability estimates for advection-diffusion equations. Nonl Diff Eqs Appl NoDEA. 2017;24:33. doi: 10.1007/s00030-017-0455-9
  • Chagas JQ, Diehl NML, Guidolin PL. Some properties for the Steklov averages, ArXiv e-prints, 1707.06368, https://arxiv.org/pdf/1707.06368.pdf, 2017.
  • Urbano JM. The method of intrinsic scaling. New York: Springer; 2008. (Lecture Notes in Mathematics; 1930).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.