Gradient estimates for variable coefficient parabolic equations and singular perturbation problems

被引：58

作者：

Caffarelli, LA

Kenig, CE

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

AMERICAN JOURNAL OF MATHEMATICS | 1998年 / 120卷 / 02期

关键词：

D O I：

10.1353/ajm.1998.0009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we prove, via monotonicity formulas, interior and boundary gradient estimates for solutions to second order parabolic equations, in divergence form, with Dini top order coefficients. We then prove uniform Lipschitz estimates for solutions of singular perturbation problems, using the previous results, and two phase monotonicity formulas.

引用

页码：391 / 439

页数：49

共 20 条

[1] ALT HW, 1981, J REINE ANGEW MATH, V325, P105
[2] VARIATIONAL-PROBLEMS WITH 2 PHASES AND THEIR FREE BOUNDARIES
ALT, HW
CAFFARELLI, LA
FRIEDMAN, A
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) : 431 - 461
[3] A GENERALIZED POINCARE INEQUALITY FOR GAUSSIAN MEASURES
BECKNER, W
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 105 (02) : 397 - 400
[4] BECKNER W, IN PRESS CONVEXITY P
[5] BERESTYCKI H, 1990, LECT NOTES PURE APPL, V122, P567
[6] ON EXTENSIONS OF BRUNN-MINKOWSKI AND PREKOPA-LEINDLER THEOREMS, INCLUDING INEQUALITIES FOR LOG CONCAVE FUNCTIONS, AND WITH AN APPLICATION TO DIFFUSION EQUATION
BRASCAMP, HJ
LIEB, EH
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 22 (04) : 366 - 389
[7] Caffarelli L. A., 1987, Rev. Mat. Iberoamericana, V3, P139
[8] FREE-BOUNDARY PROBLEM FOR THE HEAT-EQUATION ARISING IN FLAME PROPAGATION
CAFFARELLI, LA
VAZQUEZ, JL
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (02) : 411 - 441
[9] A HARNACK INEQUALITY APPROACH TO THE REGULARITY OF FREE BOUNDARIES .2. FLAT FREE BOUNDARIES ARE LIPSCHITZ
CAFFARELLI, LA
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1989, 42 (01) : 55 - 78
[10] REGULARITY THEOREMS FOR WEAK SOLUTIONS OF SOME NON-LINEAR SYSTEMS
CAFFARELLI, LA
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) : 833 - 838

← 1 2 →