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An Introduction to Variational Inequalities and Their Applications
David Kinderlehrer,Guido Stampacchia
No preview available - 2000
a.e. in Q analytic assume bilinear form boundary 6Q boundary conditions boundary value problem Brezis Chapter coercive vector field coincidence set compact conformal mapping consider converges convex set Corollary defined Definition denote the solution Dirichlet problem dx dt dx dy exists a unique f in Q follows free boundary problem given grad Hence Hilbert space Hö(Q hodograph Hölder continuous Hölder's inequality implies inequality u e Legendre transform Lemma let F Let Q Let u e linear Lipschitz function max(u maximum principle meas neighborhood nonnegative Problem 1.2 proof of Theorem prove satisfies Section sequence smooth boundary solution to Problem Stampacchia Stefan problem strongly coercive supersolution Suppose Theorem 2.1 u e H'(Q unique solution vanishes variables variational inequality variational inequality u e vector field weakly x e Q