On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients

E. Di Benedetto

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1986)

  • Volume: 13, Issue: 3, page 487-535
  • ISSN: 0391-173X

How to cite

top

Di Benedetto, E.. "On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 13.3 (1986): 487-535. <http://eudml.org/doc/83989>.

@article{DiBenedetto1986,
author = {Di Benedetto, E.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {measurable coefficients; Hölder continuity; weak solutions; principal part in divergence form},
language = {eng},
number = {3},
pages = {487-535},
publisher = {Scuola normale superiore},
title = {On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients},
url = {http://eudml.org/doc/83989},
volume = {13},
year = {1986},
}

TY - JOUR
AU - Di Benedetto, E.
TI - On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1986
PB - Scuola normale superiore
VL - 13
IS - 3
SP - 487
EP - 535
LA - eng
KW - measurable coefficients; Hölder continuity; weak solutions; principal part in divergence form
UR - http://eudml.org/doc/83989
ER -

References

top
  1. [1] N.D. Alikakos - R. Rostamian, Gradient estimates for degenerate diffusion equations II, Proc. Royal Soc. EdinburghA, 91 (1982), pp. 335-346. Zbl0523.35058MR658839
  2. [2] D.G. Aronson - J. Serrin, Local behaviour of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal., 25 (1967), pp. 81-123. Zbl0154.12001MR244638
  3. [3] E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Acc. Sci. Torino,Cl. Sci. Fis. Mat. Natur., (3) 3 (1957), pp. 25-43. Zbl0084.31901MR93649
  4. [4] E. Dibenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J., 32, no. 1 (1983), pp. 83-117. Zbl0526.35042MR684758
  5. [5] E. Dibenedetto, A boundary modulus of continuity for a class of singular parabolic equations, J. Differential Equations, 63, no. 3 (1986), pp. 418-447. Zbl0606.35044MR848277
  6. [6] E. Dibenedetto - A. Friedman, Regularity of solutions of nonlinear degenerate parabolic systems, J. Reine Angew. Math., 349 (1984), pp. 83-128. Zbl0527.35038MR743967
  7. [7] E. Dibenedetto - A. Friedman, Hölder estimates for nonlinear degenerate parabolic systems, J. Reine Math., 357 (1985), pp. 1-22. Zbl0549.35061MR783531
  8. [8] M. Giaquinta, Multiple integrals in the calculus variations and nonlinear elliptic systems, Annals of Mathematics Studies, Princeton, New Jersey (1983). Zbl0516.49003MR717034
  9. [9] M. Giaquinta - E. Giusti, On the regularity of the minima of variational integrals, Acta Math., 148 (1982), pp. 31-46. Zbl0494.49031MR666107
  10. [10] S.N. Kru, Results concerning the nature of the continuity of solutions of parabolic equations and some of their applications, Mat. Zametki, 6 (1969), pp. 97-108 (Russian). Zbl0189.10602MR249832
  11. [11] O.A. Ladyzhenskaya - N.A. Solonnikov - N.N. Ural'tzeva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, 23, Amer. Math. Soc., Providence, R.I. (1968). Zbl0174.15403
  12. [12] O.A. Ladyzhenskaya - N.N. Ural'zeva, Linear and quasilinear elliptic equations, Acadmic Press, New York (1968). Zbl0164.13002MR244627
  13. [13] J. Moser, A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., 13 (1960), pp. 457-468. Zbl0111.09301MR170091
  14. [14] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math., 14 (1961), pp. 577-591. Zbl0111.09302MR159138
  15. [15] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math., 17 (1964), pp. 101-134. Zbl0149.06902MR159139
  16. [16] J. Serrin, Local behaviour of solutions of quasilinear elliptic equations, Acta Math., 111 (1964), pp. 302-347. Zbl0128.09101MR170096
  17. [17] N.S. Trudinger, On Harnack type inequalities and their applications to quasilinear elliptic partial differential equations, Comm. Pure Appl. Math., 20 (1967), pp. 721-747. Zbl0153.42703MR226198
  18. [18] N.S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math., 21 (1968), pp. 205-226. Zbl0159.39303MR226168
  19. [19] K. Uhlenbeck, Regularity for a class of nonlinear elliptic systems, Acta Math., 138 (1977), pp. 219-240. Zbl0372.35030MR474389
  20. [20] G.M. Lieberman, Interior gradient bounds for nonuniformly parabolic equations, Indiana Univ. Math. J., 32, no. 4 (1983), pp. 679-701. Zbl0491.35021MR703286

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.