Local regularity results for some parabolic equations

Houston Journal of Mathematics

Volumn 25, Issue 4, 1999, Pages 769-792

  Porzio, Maria Michaela ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Local regularity; Nonlinear parabolic equations; Unbounded solutions

Indexed keywords

EID: 0040631553     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. D.G. Aronson, On the Green's function for second order parabolic differential equations with discontinuous coefficients , Bulletin of the American Mathematical Society 69, 841-847 (1963)
2. D.G. Aronson, J. Serrin, Local behaviour of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal., 25 (1967), 81-122.
3. L. Boccardo, Existence and regularity results for quasilinear parabolic equations, Proceedings Trieste, 1995.
4. L. Boccardo, A. Dall'Aglio, T. Gallouët, L. Orsina, Regularity results for nonlinear parabolic equations, to appear on Adv. Math. Sci. Appl.
5. L. Boccardo, D. Giachetti, Alcune osservazioni sulla regolarità delle soluzioni di problemi non-lineari e applicazioni, Ricerche di Matematica, XXXIV, (1985).
6. s-regularity of solutions of some nonlinear elliptic problems, preprint.
7. E. Di Benedetto, Degenerate parabolic equations, Springer-Verlag, New York, (1993).
8. M. Giaquinta, Multiple integrals in the Calculus of Variations and nonlinear elliptic systems, Princeton University Press, (1983).
9. D. Giachetti, M.M. Porzio, Local regularity results for minima of functional of the Calculus of Variation, to appear on Nonlinear Analysis T.M.A.
10. F. Guglielmino, Sulla regolarizzazione delle soluzioni deboli dei problemi al contorno per operatori parabolici , Ricerche di Matematica 12, 44-66, 140-150 (1963).
11. A.V. Ivanov, A priori estimates for solutions of linear equations of second order of elliptic and parabolic type , Doklady Akademii Nauk S.S.S.R. 161, 1270-1273 (1965).
12. A.V. Ivanov, O. A. Ladyzenskaja, A.L. Treskunov, N.N. Uralcéva, Certain properties of generalized solutions of parabolic equations of second order , Doklady Akademii Nauk S.S.S.R. 168, 17-20 (1966).
13. S.N. Kruzkov, A priori estimates and certain properties of solutions of elliptic and parabolic equations, Matematiceskii Sbornik 65, 522-570 (1964).
14. O. A. Ladyzenskaja, N.A. Solonnikov, N.N. Uralcéva, Linear and quasilinear equations of parabolic type, Trans Math. Monogr., Am. Math. Soc. 23, Providence, RI (1968).
15. O. A. Ladyzenskaja, N.N. Uralcéva, A boundary value problem for linear and quasilinear parabolic equations I, II, III. Izvestija akademii Nauk S.S.S.R. Serija Matematiceskaja 26, 5-52 (1962); 26, 753-780 (1962); 27, 161-240 (1963).
16. O. A. Ladyzenskaja, N.N. Uralcéva, A boundary value problem for linear and quasilinear parabolic equations I, II, III. Izvestija akademii Nauk S.S.S.R. Serija Matematiceskaja 26, 5-52 (1962); 26, 753-780 (1962); 27, 161-240 (1963).
17. O. A. Ladyzenskaja, N.N. Uralcéva, A boundary value problem for linear and quasilinear parabolic equations I, II, III. Izvestija akademii Nauk S.S.S.R. Serija Matematiceskaja 26, 5-52 (1962); 26, 753-780 (1962); 27, 161-240 (1963).
18. J.L. Lions, Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, (1969).
19. J. Moser, A Harnack inequality for parabolic differential equations, Communications on Pure and Applied Mathematics 17, 101-134 (1964); Correction ibid. 20, 231-236 (1967).
20. J. Moser, A Harnack inequality for parabolic differential equations, Communications on Pure and Applied Mathematics 17, 101-134 (1964); Correction ibid. 20, 231-236 (1967).