The $L^p$ solvability of the Dirichlet problems for parabolic equations

• Autorzy: Xiang Xing Tao
• Języki publikacji: EN

Abstrakty

EN

For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of $L^p$ solvability of the Dirichlet problems.

Słowa kluczowe

EN

parabolic equation; $L^p$ solvability; Dirichlet problems; Lip(1,1/2) cylinder

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 35K20: Initial-boundary value problems for second-order parabolic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 139
• Numer: 1
• Strony: 69-80

Daty

wydano

2000

otrzymano

1998-11-10

Twórcy

autor

Xiang Xing Tao

• Department of Mathematics, Ningbo University, Ningbo, Zhejiang, 315211, P.R. China.

Bibliografia

• [A] D. G. Aronson, Non-negative solutions of linear parabolic equations, Ann Scuola Norm. Sup. Pisa 22 (1968), 607-694.
• [Do] J. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, 1984.
• [FGS] E. B. Fabes, N. Garofalo and S. Salsa, A backward Harnack inequality and Fatou theorems for nonnegative solutions of parabolic operators, Illinois J. Math. 30 (1986), 536-565.
• [FKP] R. A. Fefferman, C. E. Kenig and J. Pipher, The theory of weights and the Dirichlet problems for elliptic equations, Ann. of Math. 134 (1991), 65-124.
• [K] C. E. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS, 1994.
• [L] N. L. Lim, The $L^p$ Dirichlet problem for divergence form elliptic operators with non-smooth coefficients, J. Funct. Anal. 138 (1996), 503-543.
• [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.
• [M] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134; correction, ibid. 20 (1967), 231-236.
• [N] K. Nyström, The Dirichlet problem for second order parabolic operators, Indiana Univ. Math. J. 46 (1997), 183-245.
• [St] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, NJ, 1993.