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Keywords:
regularity of weak solutions; parabolic systems
regularity of weak solutions; parabolic systems
Summary:
A vector valued function $u=u(x,t)$, solution of a quasilinear parabolic system cannot be too close to a straight line without being regular.
References:
[1] Giusti E., Modica G.: A note on regular points for solutions of elliptic systems. Manusc. Math. 29 (1979), 417-426. MR 0545051 | Zbl 0419.35015
[2] Giusti E.: Regolarita partiale delle soluzioni di sistemi ellittici quasilineari di ordine arbitrario. Ann. Scuola Norm. Sup. Pisa 23 (1969), 115-141. MR 0247258
[3] Campanato S.: Equazioni paraboliche del secondo ordine e spazi ${\Cal L}^{2,\Theta}{(Ømega,\delta)}$. Ann. Mat. Pura Appl. 73 (1966), 55-102. MR 0213737
[4] Giaquinta M., Giusti E.: Partial regularity for the solutions to nonlinear parabolic systems. Ann. Mat. Pura Appl. 47 (1973), 253-266. MR 0338568 | Zbl 0276.35062
[5] Ladyzhenskaya O.A., Solonnikov V.A., Uralceva N.N.: Linear and quasilinear equations of parabolic type. Translations of Math. Monographs 23, Providence, Rhode Island: AMS 1968.
[6] Giaquinta M., Struwe M.: On the partial regularity of weak solutions of nonlinear parabolic systems. Math. Z. 179 (1982), 437-451. MR 0652852
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