Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations

  • Ilya J. Bakelman


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.


Convex Function Dirichlet Problem Convex Cone Supporting Hyperplane Geometric Concept 
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© Springer-Verlag Berlin Heidelberg 1994

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  • Ilya J. Bakelman

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