On doubling properties for non-negative weak solutions of elliptic and parabolic PDE

被引：0
作者：
Kazuhiro Kurata
机构：
[1] Tokyo Metropolitan University,Department of Mathematics
来源：
Israel Journal of Mathematics | 2000年 / 115卷
关键词：
Weak Solution; Elliptic Equation; Unique Continuation; Degenerate Parabolic Equation; Doubling Property;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper we study quantitative properties of non-negative (super) solutions for elliptic and parabolic partial differential equations of second order with strongly singular coefficients, in which we cannot expect Harnack's inequality in general. We show the doubling property ofuδ with some small exponent 1>δ>0 for non-negative weak supersolutionsu. Furthermore, we show the doubling property ofuq with large exponent 2(n+2)/n≥q>0 for non-negative weak solutionsu of parabolic equations.
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页码：285 / 302
页数：17
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共 26 条
[1]  
Aronson D. G.(1967)Local behavior of solutions of quasilinear parabolic equations Archive for Rational Mechanics and Analysis 25 81-122
[2]  
Serrin J.(1988)Harnack's inequality for Schrödinger operators and the continuity of solutions Proceedings of the American Mathematical Society 98 415-425
[3]  
Chiarenza F.(1984)A Harnack inequality for degenerate parabolic equations Communications in Partial Differential Equations 9 719-749
[4]  
Fabes E.(1985)A remark on a Harnack inequality for degenerate parabolic equations Rendiconti del Seminario Matematico della Università di Padova 73 179-190
[5]  
Garofalo N.(1985)L Communications in Partial Differential Equations 10 1077-1116
[6]  
Chiarenza F.(1982)-estimate for fractional integrals and Sobolev inequalities with applications to Schrödinger operators Communications in Partial Differential Equations 7 77-116
[7]  
Serapinoi R.(1986)The local regularity of solutions of degenerate elliptic equations Indiana University Mathematics Journal 35 246-268
[8]  
Chiarenza F.(1987)Monotonicity properties of variational integrals. A Communications on Pure and Applied Mathematics 40 347-366
[9]  
Serapinoi R.(1994) weights and unique continuation Indiana University Mathematics Journal 43 411-440
[10]  
Chanillo S.(1993)Unique continuation for elliptic operators: A geometric-variational approach Communications in Partial Differential Equations 18 1161-1189
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