Title :
Variational Inequality on a Class of Variable Coefficient Elliptic Boundary Value Problems
Author :
Li, Baofeng ; Wang, Donghua
Author_Institution :
Dept. of Math. & Inf. Sci., Tangshan Teachers Coll., Tangshan, China
Abstract :
Contact problem widely exists in diverse fields. Many contact problems are induced to boundary values and variational problem. Boundary variational inequality methods have been playing crucial roles in contact problem field, inducing all the boundary conditions and contact conditions to one variational inequality and making the theoretical analysis very easy. There are many articles using variational inequalities to study elliptic boundary value problems. And most of the problems are induced to a Laplace equation or Poisson equation and then to solve first or second boundary value problem which are the constant coefficient elliptic partial differential equations. Corresponding with a class of variable coefficient elliptic boundary value problems, a variational inequality is obtained using Green formula. At the same time the equivalence of the two problems (that is a variable coefficient elliptic boundary value problem and equal variational inequality) and the existence and uniqueness of solutions in this paper are proved.
Keywords :
Laplace equations; Poisson equation; boundary-value problems; elliptic equations; variational techniques; Green formula; Laplace equation; Poisson equation; boundary variational inequality method; constant coefficient elliptic partial differential equations; contact problem; contact problem field; elliptic boundary value problem; variable coefficient elliptic boundary value problem; Boundary value problems; Convex functions; Equations; Integral equations; Laplace equations; Poisson equations; existence and uniqueness of solutions; variable coefficient elliptic boundary value problems; variational inequality;
Conference_Titel :
Cryptography and Network Security, Data Mining and Knowledge Discovery, E-Commerce & Its Applications and Embedded Systems (CDEE), 2010 First ACIS International Symposium on
Conference_Location :
Qinhuangdao
Print_ISBN :
978-1-4244-9595-5
DOI :
10.1109/CDEE.2010.39