The L p solvability of the Dirichlet problems for parabolic equations

Xiang Tao

Studia Mathematica (2000)

  • Volume: 139, Issue: 1, page 69-80
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Tao, Xiang. "The $L^p$ solvability of the Dirichlet problems for parabolic equations." Studia Mathematica 139.1 (2000): 69-80. <http://eudml.org/doc/216711>.

@article{Tao2000,
abstract = {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.},
author = {Tao, Xiang},
journal = {Studia Mathematica},
keywords = {parabolic equation; $L^p$ solvability; Dirichlet problems; Lip(1,1/2) cylinder; second-order parabolic divergence form operators; time-dependent coefficients; preservation of solvability},
language = {eng},
number = {1},
pages = {69-80},
title = {The $L^p$ solvability of the Dirichlet problems for parabolic equations},
url = {http://eudml.org/doc/216711},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Tao, Xiang
TI - The $L^p$ solvability of the Dirichlet problems for parabolic equations
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 1
SP - 69
EP - 80
AB - 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.
LA - eng
KW - parabolic equation; $L^p$ solvability; Dirichlet problems; Lip(1,1/2) cylinder; second-order parabolic divergence form operators; time-dependent coefficients; preservation of solvability
UR - http://eudml.org/doc/216711
ER -

References

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  1. [A] D. G. Aronson, Non-negative solutions of linear parabolic equations, Ann Scuola Norm. Sup. Pisa 22 (1968), 607-694. Zbl0182.13802
  2. [Do] J. Doob, Classical Potential Theory and its Probabilistic Counterpart, Springer, 1984. 
  3. [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. Zbl0625.35006
  4. [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. Zbl0770.35014
  5. [K] C. E. Kenig, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS, 1994. 
  6. [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. Zbl0856.35035
  7. [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. Zbl0236.26016
  8. [M] J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134; correction, ibid. 20 (1967), 231-236. 
  9. [N] K. Nyström, The Dirichlet problem for second order parabolic operators, Indiana Univ. Math. J. 46 (1997), 183-245. Zbl0878.35010
  10. [St] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, NJ, 1993. 

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