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On Uniqueness of Solutions to the Boundary Value Problems on the Sierpiński Gasket
Numerical Functional Analysis and Optimization ( IF 1.2 ) Pub Date : 2021-05-28 , DOI: 10.1080/01630563.2021.1931310 Robert Stegliński 1
中文翻译:
谢尔宾斯基垫片边值问题解的唯一性
更新日期:2021-06-29
Numerical Functional Analysis and Optimization ( IF 1.2 ) Pub Date : 2021-05-28 , DOI: 10.1080/01630563.2021.1931310 Robert Stegliński 1
Affiliation
Abstract
Using the monotonicity methods, we obtain conditions for the existence of the unique weak solution of Dirichlet problem
considered on the Sierpiński gasket. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are also given. We also consider a problem with parameters and we prove the theorem about continuous dependence on parameters.
中文翻译:
谢尔宾斯基垫片边值问题解的唯一性
摘要
使用单调性方法,我们获得了狄利克雷问题唯一弱解存在的条件
考虑在谢尔宾斯基垫片上。我们主张某些假设的最优性。还给出了一些李雅普诺夫型不等式。我们还考虑了一个参数问题,并证明了关于参数连续依赖的定理。