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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A priori estimates for quasilinear degenerate parabolic equations
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by Maria Manfredini and Andrea Pascucci PDF
Proc. Amer. Math. Soc. 131 (2003), 1115-1120 Request permission

Abstract:

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.
References
  • F. Antonelli, A. Pascucci, On the viscosity solutions of a stochastic differential utility problem, to appear in J. Differential Equations.
  • G. Barles, A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations 4 (1991), no. 2, 241–262. MR 1081182
  • S. Bernstein, Sur la généralisation du probléme de Dirichlet, I, Math. Ann., 62, (1906), 253–271.
  • Giovanna Citti, Andrea Pascucci, and Sergio Polidoro, Regularity properties of viscosity solutions of a non-Hörmander degenerate equation, J. Math. Pures Appl. (9) 80 (2001), no. 9, 901–918 (English, with English and French summaries). MR 1865380, DOI 10.1016/S0021-7824(01)01223-5
  • G. Citti, M. Manfredini, A degenerate parabolic equation arising in image processing, to appear in Commun. Appl. Anal.
  • M. Escobedo, J. L. Vázquez, and Enrike Zuazua, Entropy solutions for diffusion-convection equations with partial diffusivity, Trans. Amer. Math. Soc. 343 (1994), no. 2, 829–842. MR 1225573, DOI 10.1090/S0002-9947-1994-1225573-2
  • David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. MR 1814364
  • Gerhard Huisken, Nonparametric mean curvature evolution with boundary conditions, J. Differential Equations 77 (1989), no. 2, 369–378. MR 983300, DOI 10.1016/0022-0396(89)90149-6
  • A. V. Ivanov, Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, Proc. Steklov Inst. Math. 1(160) (1984), xi+287. A translation of Trudy Mat. Inst. Steklov 160 (1982); Translated from the Russian by J. R. Schulenberger. MR 753230
  • O.A. Ladyzhenskaya, N.N. Ural’tseva, A boundary value problem for linear and quasilinear parabolic equations I, II, (Russian, English) Am. Math. Soc., Transl., II. Ser. 47, 217-299 (1965); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 26, 5-52, 753-780 (1962).
  • O.A. Ladyzhenskaya, N.N. Ural’tseva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monographs 23. Providence, RI: American Mathematical Society (1968).
  • Gary M. Lieberman, Second order parabolic differential equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1996. MR 1465184, DOI 10.1142/3302
  • Gary M. Lieberman, Gradient estimates for a new class of degenerate elliptic and parabolic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994), no. 4, 497–522. MR 1318770
  • A. Pascucci, S. Polidoro, On the Cauchy problem for a nonlinear ultraparabolic equation, preprint
  • James Serrin, Gradient estimates for solutions of nonlinear elliptic and parabolic equations, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Academic Press, New York, 1971, pp. 565–601. MR 0402274
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Additional Information
  • Maria Manfredini
  • Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
  • MR Author ID: 321628
  • Email: manfredi@dm.unibo.it
  • Andrea Pascucci
  • Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
  • Email: pascucci@dm.unibo.it
  • Received by editor(s): October 15, 2001
  • Published electronically: November 13, 2002
  • Additional Notes: This work was supported by the University of Bologna, funds for selected research topics
  • Communicated by: David S. Tartakoff
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1115-1120
  • MSC (2000): Primary 35K55; Secondary 35K65
  • DOI: https://doi.org/10.1090/S0002-9939-02-06922-8
  • MathSciNet review: 1948102