Multiple Integrals in the Calculus of Variations (Google eBook)
Springer Science & Business Media, Nov 3, 2009 - Calculus of variations - 517 pages
Suitable for those concerned with multiple integral variational problems and with elliptic partial differential equations, this book presents a comprehensive treatise of the theory of multiple integral variational problems.
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absolutely continuous analytic assume B(xo B(xq boundary values bounded operator Chapter choose class C1 compact conclude constant continuous on G converges uniformly convex coordinate patch corresponding D C C G Definition denote depends derivatives diffeomorphism differential equations Dirichlet domain G elliptic equicontinuous Euler's equation existence theorem f satisfies finite number following theorem follows easily follows from Theorem formula geodesic given harmonic hence Holder inequality holds homogeneous of degree hypotheses inequality interior Lemma lim inf linear Lipschitz domain lower semicontinuity manifold mapping Math minimizing mollified Moreover Morrey Multiple Integrals neighborhood norm notation obtain open set orthogonal partition of unity problem proof of Theorem quasi-convex replaced respect result follows Riemannian manifold satisfy the conditions sequence space subset sufficient Suppose G surface theory tion uniformly bounded vanishes variational weak convergence