On some parabolic variational problems with quadratic growth
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 13 (1986) no. 2, pp. 193-223. 
@article{ASNSP_1986_4_13_2_193_0,
     author = {Tolksdorf, Peter},
     title = {On some parabolic variational problems with quadratic growth},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {193--223},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 13},
     number = {2},
     year = {1986},
     mrnumber = {876122},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1986_4_13_2_193_0/}
}
TY  - JOUR
AU  - Tolksdorf, Peter
TI  - On some parabolic variational problems with quadratic growth
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1986
SP  - 193
EP  - 223
VL  - 13
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1986_4_13_2_193_0/
LA  - en
ID  - ASNSP_1986_4_13_2_193_0
ER  - 
%0 Journal Article
%A Tolksdorf, Peter
%T On some parabolic variational problems with quadratic growth
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1986
%P 193-223
%V 13
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1986_4_13_2_193_0/
%G en
%F ASNSP_1986_4_13_2_193_0
Tolksdorf, Peter. On some parabolic variational problems with quadratic growth. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 13 (1986) no. 2, pp. 193-223. http://www.numdam.org/item/ASNSP_1986_4_13_2_193_0/

[1] H.W. Alt - S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Preprint Nr. 568 des SFB 72, Universität Bonn, 1983. | MR

[2] L.A. Caffarelli, Regularity theorems for weak solutions of some nonlinear systems, Comm. Pure Appl. Math., 35 (1982), pp. 771-782. | MR | Zbl

[3] E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., Ser. 3, 3 (1957), pp. 25-43. | MR | Zbl

[4] M. Giaquinta - M. Struwe, An optimal regularity result for a class of quasilinear parabolic systems, Manuseripta Math., 36 (1981), pp. 223-239. | MR | Zbl

[5] M. Giaquinta - M. Struwe, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z., 179 (1982), pp. 437-451. | MR | Zbl

[6] D. Gilbarg - N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, 1977. | MR | Zbl

[7] R.S. Hamilton, Harmonic maps of manifolds with boundary, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1975. | MR | Zbl

[8] S. Hildebrandt - K.O. Widman, Some regularity results for quasilinear elliptic systems of second order, Math. Z., 142 (1975), pp. 67-86. | MR | Zbl

[9] S. Hildebrandt - K.O. Widman, On the Hölder-continuity of weak solutions of quasilinear elliptic systems of second order, Ann. Scuola Norm. Sup. Pisa Cl, Sci., 4 (1977), pp. 145-178. | Numdam | MR | Zbl

[10] S. Hildebrandt - K.O. Widman, Variational inequalities for vector-valued functions, J. Reine Angew. Math., 309 (1979), pp. 191-220. | MR | Zbl

[11] J. Jost, Ein Existeuzbeweis, für harmonische Abbitdungen, die ein Dirichlet-problem lösen, mittels der Methode des Warmeflusses, Manuscripta Math., 34 (1981), pp. 17-25. | MR | Zbl

[12] N. Kilimann, Ein Maximumprinzip für nichtlineare parabolische Systeme, Math. Z., 171 (1980), pp. 227-230. | MR | Zbl

[13] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Uraltseva, Linear and quasilinear equations of parabolic type, Translations Math. Monograph, 23, Amer. Math. Soc., Providence, R.I., 1968. | Zbl

[14] O.A. Ladyzhenskaya - N.N. Uraltseva, Linear and quasilinear elliptic equations, Academic Press, New York, 1968. | MR | Zbl

[15] M. Struwe, On the Hölder-continuity of bounded weak solutions of quasilinear parabolic systems, Monograph Math., 35 (1981), pp. 223-239. | MR | Zbl

[16] M. Struwe, A counterexample in regularity theory for parabolic systems, Comm, Math. Univ. Carol., to appear. | MR

[17] M. Struwe - M.A. Vivaldi, On the regularity of quasilinear parabolic variational inequalities, preprint.

[18] P. Tolksdorf, A new proof of a regularity theorem, Invent. Math., 71 (1983), pp. 43-49. | MR | Zbl

[19] P. Tolksdorf, A Strong Maximum Principle and regularity for harmonic mappings, preprint. | MR

[20] F. Treves, Basic linear partial differential equations, Academic Press, New York, 1975. | MR | Zbl

[21] W V. Wahl, Klassische Lösbarkeit im Groβen für nichtlineare parabolische Systeme und das Verhalten der Losungen für t → ∞, Preprint Nr. 395 des SFB 72, Universität Bonn, 1980.