Convex Functions Methods in the Dirichlet Problem for Euler—Lagrange Equations

Ilya J. Bakelman

A chapter in Variational Methods for Free Surface Interfaces, 1987, pp 127-137 from Springer

Abstract: Abstract In this paper we investigate a priori estimates for solutions of the second order elliptic E—L equations,* whose gradients satisfy some prescribed limitations. Such problems arise from the relativity theory and continuous mechanics and can be described in terms of variational problems for the n-dimensional multiple integrals 1 $$\int_{B}\, F(x, u, Du)\, dx$$ whose integrands F(x, u, p) are defined only for vectors p belonging to prescribed domain G in R n . If G coincides with the whole space R n , then we do not have any prescribed limitations for the gradient of desired solutions for the E—L equation corresponding to the functional (1). This most simple case was investigated in our paper [1].

Keywords: Dirichlet Problem; Minkowski Space; Tangential Mapping; Curvature Equation; Spacelike Hypersurface (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-4656-5_15

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DOI: 10.1007/978-1-4612-4656-5_15

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