Double phase obstacle problems with variable exponent
Double phase obstacle problems with variable exponent
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DOI：
10.57262/ade027-0910-611
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发表时间：
2022-09
影响因子：
1.4
通讯作者：
Shengda Zeng;Vicentiu D. Rădulescu;Patrick Winkert
中科院分区：
文献类型：
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作者：
Shengda Zeng;Vicentiu D. Rădulescu;Patrick Winkert
.研究了一类由变指数双相微分算子、障碍项和多值反应项驱动的拟线性椭圆包含问题.利用多值伪单调算子混合变分不等式的一个存在性结果和非光滑分析理论，研究了问题解集的非空性、有界性和闭性.在本文的第二部分，我们提出了一些近似问题的收敛性分析。更精确地说，当障碍函数近似由一个合适的序列，应用广义惩罚技术，我们引入了一个家庭的扰动问题没有相关的约束，我们的问题，并证明了原问题的解集可以接近的解集的扰动问题的Kuratowski意义。
. This paper is devoted to the study of a quasilinear elliptic inclusion problem driven by a double phase differential operator with variable exponents, an obstacle effect and a multival-ued reaction term with gradient dependence. By using an existence result for mixed variational inequalities with multivalued pseudomonotone operators and the theory of nonsmooth analysis, we examine the nonemptiness, boundedness and closedness of the solution set to the problem under consideration. In the second part of the paper we present some convergence analysis for approximated problems. To be more precise, when the obstacle function is approximated by a suitable sequence, applying a generalized penalty technique, we introduce a family of perturbed problems without constraints associated to our problem and prove that the solution set of the original problem can be approached by the solution sets of the perturbed problems in the sense of Kuratowski.