Abstract quasi-variational inequalities of elliptic type and applications
Abstract quasi-variational inequalities of elliptic type and applications
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椭圆型抽象拟变分不等式及其应用
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发表时间：
2009
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通讯作者：
Yusuke Murase
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作者：
Yusuke Murase
椭圆型拟变分不等式及其应用千叶大学研究生院理工学研究科数学系，地址：日本千叶市稻上区弥生町1-33，邮编：263-8522电子邮件：ym@graduate.chiba-u.jp摘要.在自反Banach空间中研究了一类椭圆型拟变分不等式。QVI的概念最早由A. Bensoussan和J.L. Lions [2]和它的一般理论已经被许多数学家所发展，例如，见[6，7，9，13]和一本专著[1]。本文推广了文[14]中的存在定理。在我们的处理中，我们采用紧性方法沿着与单调型的非线性多值算子的收敛的概念（参见。[11]）。我们将证明这类QVI的一个抽象的存在性结果，并给出QVI在椭圆型偏微分算子中的一些应用。在自反Banach空间中研究了一类椭圆型拟变分不等式。QVI的概念最早由A. Bensoussan和J.L. Lions [2]和它的一般理论已经被许多数学家所发展，例如，见[6，7，9，13]和一本专著[1]。本文推广了文[14]中的存在定理。在我们的处理中，我们采用紧性方法沿着与单调型的非线性多值算子的收敛的概念（参见。[11]）。我们将证明这类QVI的一个抽象的存在性结果，并给出QVI在椭圆型偏微分算子中的一些应用。
Quasi-Variational Inequalities of Elliptic type and Applications Yusuke Murase Department of Mathematics, Graduate School of Science and Technology Chiba University 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan E-Mail: ym@graduate.chiba-u.jp Abstract. A class of quasi-variational inequalities (QVI) of the elliptic type is studied in reflexive Banach spaces. The concept of QVI was ealier introduced by A. Bensoussan and J. L. Lions [2] and its general theory has been evolved by many mathematicians, for instance, see [6,7,9,13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. [11]). We shall prove an abstract existence result for our class of QVI’s, and moreover, give some applications to QVI’s for elliptic partial differential operators. A class of quasi-variational inequalities (QVI) of the elliptic type is studied in reflexive Banach spaces. The concept of QVI was ealier introduced by A. Bensoussan and J. L. Lions [2] and its general theory has been evolved by many mathematicians, for instance, see [6,7,9,13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. [11]). We shall prove an abstract existence result for our class of QVI’s, and moreover, give some applications to QVI’s for elliptic partial differential operators.