一类奇异p-laplacian方程解的存在性与正则性

发布时间：2018-04-22 22:14

本文选题：p-laplacian + 伪单调算子　；参考：《大连理工大学》2016年硕士论文

【摘要】：本文讨论下列奇异p-laplacian问题的解的存在性及正则性。本文通过逼近方法得到了逼近解及解的先验估计,然后利用弱收敛方法得到了问题(P1)的解。本文共分为四章。第一章绪论,主要介绍了论文的研究背景、已有的工作以及本文研究的主要问题及结果。第二章预备知识,给出了证明过程中需要用到的定义、引理及记号。第三章和第四章为本文的主要结果及证明。第三章给出了当0μCN,p时问题(P1)的解的存在性及正则性。第四章给出了当μ0时问题(P1)的解的存在性及正则性。
[Abstract]:In this paper, we discuss the existence and regularity of solutions for the following singular p-laplacian problems. In this paper, a priori estimate of the approximate solution and solution is obtained by means of the approximation method, and then the solution of the problem / P _ 1 is obtained by using the weak convergence method. This paper is divided into four chapters. The first chapter is introduction, mainly introduces the research background, the existing work and the main problems and results of this paper. In the second chapter, the definitions, Lemma and notation are given. The third and fourth chapters are the main results and proofs of this paper. In chapter 3, we give the existence and regularity of the solution of the problem P _ (1) when 0 渭 CNP. In chapter 4, we give the existence and regularity of the solution of the problem P _ 1 when 渭 _ 0.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175

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