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Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations

  • Ilya J. Bakelman

Abstract

This chapter is concerned with global connections between the integrand F(x, u,p) of n-multiple integrals
$$I\left( u \right) = \int_{B} {F\left( {x,u\left( x \right),Du\left( x \right)} \right)} dx $$
and a priori estimates for solutions of the corresponding Euler-Lagrange equations, whose gradients satisfy some prescribed limitations. Such problems arise in the calculus of variations, differential geometry and continuum mechanics. Typical examples of these problems are presented in §§ 23, 24. Some of these estimates are called geometric maximum principles for variational problems.

Keywords

Convex Function Dirichlet Problem Convex Cone Supporting Hyperplane Geometric Concept 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Ilya J. Bakelman

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