On the Schauder estimates of solutions to parabolic equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, p. 1-26
@article{ASNSP_1998_4_27_1_1_0,
author = {Han, Qing},
title = {On the Schauder estimates of solutions to parabolic equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 27},
number = {1},
year = {1998},
pages = {1-26},
zbl = {0954.35034},
mrnumber = {1658901},
language = {en},
url = {http://www.numdam.org/item/ASNSP_1998_4_27_1_1_0}
}

Han, Qing. On the Schauder estimates of solutions to parabolic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 27 (1998) no. 1, pp. 1-26. http://www.numdam.org/item/ASNSP_1998_4_27_1_1_0/

[1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727; II, Comm. Pure Appl. Math. 17 (1964), 35-92. | MR 125307 | Zbl 0093.10401

[2] G. Alessandrini - S. Vessella, Local Behavior of solutions to parabolic equations, Comm. Partial Differential Equations 13 (9) (1988), 1041-1058. | MR 946281 | Zbl 0649.35040

[3] L. Bers, Local behavior of solution of general linear elliptic equations, Comm. Pure Appl. Math. 8 (1955), 473-496. | MR 75416 | Zbl 0066.08101

[4] L.A. Caffarelli, Interior a priori estimates for solutions of fully nonlinear equations, Ann. of Math. 130 (1989), 189-213. | MR 1005611 | Zbl 0692.35017

[5] S. Campanato, Equazioni paraboliche del secondo ordine e apazi L 2,θ (Ω, δ), Ann. Mat. Pura . Appl., 73 (1966), 55-102. | Zbl 0144.14101

[6] L.A. Caffarelli - A. Friedman, Partial regularity of the Zero-set of solutions of linear and superlinear elliptic equations, J. Differential Equations 60 (1985), 420-433. | MR 811775 | Zbl 0593.35047

[7] E. Fabes, Singular integrals and partial differential equations of parabolic type, Studia Math. 28 (1966), 81-131. | MR 213744 | Zbl 0144.35002

[8] A. Friedman, "Partial Differential Equations of Parabolic Type", Prentice-Hall, Englewood Cliffs, 1964. | MR 181836 | Zbl 0144.34903

[9] N. Garofalo - F.-H. Lin, Monotonicity properties of variational integrals, Ap weights and unique continuation, Indiana Univ. Math J. 35 (1986), 245-267. | MR 833393 | Zbl 0678.35015

[10] D. Gilbarg - N. Trudinger, "Elliptic Partial Differential Equations of Second Order", Second Edition, Springer, Berlin, 1983. | MR 737190 | Zbl 0562.35001

[11] Q. Han, A priori estimate on asymptotic polynomials and its application, J. Geom. Analysis, to appear.

[12] Q. Han - F.-H. Lin, Nodal Sets of Solutions of Parabolic Equations, II, Comm. Pure Appl. Math. (1994), 1219-123 8. | MR 1290401 | Zbl 0807.35052

[13] B.F. Jones, Jr., A class of singular integrals, Amer. J. Math. 86 (1964), 441-462. | MR 161099 | Zbl 0123.08501

[14] N.V. Krylov, "Nonlinear Elliptic and Parabolic Equations of Second Order", Mathematics and its Applications, 1985. | Zbl 0619.35004

[15] F.-H. Lin, Nodal sets of solutions of elliptic and parabolic equations, Comm. Pure Appl. Math. 45 (1991), 287-308. | MR 1090434 | Zbl 0734.58045

[16] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Ural'Tseva, "Linear and Quasilinear Parabolic Equations", Nauka, Moscow, 1967. English transl., AMS, Providence, 1968.

[17] M. Stein, "Singular Integrals and the Differentiability Properties of Functions ", Princeton University Press, 1970. | MR 290095 | Zbl 0207.13501

[18] L. Wang, On the regularity theory offully nonlinear parabolic equations. I, Comm. Pure Appl. Math. 45 (1992), 27-76; II, Comm. Pure Appl. Math. 45 (1992), 141-178. | MR 1135923 | Zbl 0774.35042

[19] H. Yin, L2,μ (Q) estimates for parabolic equations and applications, J. Partial Differential Equations 10 (1997), 31-44. | Zbl 0891.35021