双非线性带权抛物型方程解的正则性

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-05 DOI:10.1090/s0077-1554-2014-00237-5

M. D. SURNACH¨EV, Boris Moiseevich Levitan

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引用次数: 10

摘要

．研究了一类具有重退化和权的非线性抛物型方程解的局部正则性。我们对权值施加p -可容许性条件;特别是，这允许在Muckenhoupt类A p中的权重。我们证明了解是局部H′olderian的，不受符号为常数的限制。我们证明了一个非负解的哈纳克不等式。在接近线性的情况下，我们检验了常数作为参数的稳定性。

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Regularity of solutions of parabolic equations with a double nonlinearity and a weight

. We study local regularity of solutions of nonlinear parabolic equations with a double degeneracy and a weight. We impose the condition of p -admissibility on the weight; in particular this allows weights in the Muckenhoupt classes A p . We prove that solutions are locally H¨olderian without any restriction on the sign being constant. We prove a Harnack inequality for nonnegative solutions. We examine the stability of the constants as the parameters in the equation approach the linear case.

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.