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On the local behavior of solutions of singular parabolic equations

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Bibliography

  1. D. G. Aronson & J. Serrin, Local behavior of solutions of quasi-linear parabolic equations, Arch. Rational Mech. Anal. 25 (1967) pp. 81–123.

    Google Scholar 

  2. Ph. Bènilan & M. G. Crandall, Regularizing effects of homogeneous evolution equations, MRC Technical Report # 2076, Madison, Wi. 1980.

  3. Y. Z. Chen, Hölder continuity of the gradient of solutions of non linear degenerate parabolic systems, Acta Mat. Sinica, New Series 2, # 4 (1986) pp. 309–331.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. E. Di Benedetto, On the local behavior of solutions of degenerate parabolic equations with measurable coefficients, Ann. Sc. Norm. Sup. Pisa Cl. Scienze Serie IV, 13 no. 3 (1986) pp. 487–535.

    Google Scholar 

  6. E. Di Benedetto, 344-01 local regularity of weak solutions of degenerate elliptic equations. Non linear Analysis TMA 7 # 8 (1983) pp. 827–850.

    Google Scholar 

  7. E. Di Benedetto & A. Friedman, Hölder estimates for non linear degenerate parabolic systems, J. Reine Angew. Math. 357 (1985) pp. 1–22.

    Google Scholar 

  8. O. A. Ladyzhenskaya, N. A. Solonnikov, & N. N. Ural'tzeva, Linear and quasilinear equations of parabolic type, Transl. Math. Mono. # 23 Amer. Math. Soc. Providence R.I. (1968).

  9. J.-L. Lions, Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod Paris 1969.

    Google Scholar 

  10. J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), pp. 101–134.

    Google Scholar 

  11. N. S. Trudinger, Pointwise estimates and quasi-linear parabolic equations, Comm. Pure Appl. Math. 21 (1968) pp. 205–226.

    Google Scholar 

  12. Kwong, Ying C., Interior and boundary regularity of solutions to a plasma problem (to appear in Proceedings of AMS).

  13. E. S. Sabinina, A class of non-linear degenerate parabolic equations, Sov. Math. Doklady 143 (1962) pp. 495–498.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, Peoples Republic of China

    Chen Ya-zhe & Emmanuele Di Benedetto

  2. Department of Mathematics, Northwestern University, Evanston, Illinois

    Chen Ya-zhe & Emmanuele Di Benedetto

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  1. Chen Ya-zhe
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  2. Emmanuele Di Benedetto
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Communicated by E. Giusti

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Ya-zhe, C., Di Benedetto, E. On the local behavior of solutions of singular parabolic equations. Arch. Rational Mech. Anal. 103, 319–345 (1988). https://doi.org/10.1007/BF00251444

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