Skip to main content

Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations

  • Chapter
  • 365 Accesses

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-69881-1_7
  • Chapter length: 53 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   84.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-69881-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   109.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bakelman, I.J. (1994). Geometric Concepts and Methods in Nonlinear Elliptic Euler-Lagrange Equations. In: Convex Analysis and Nonlinear Geometric Elliptic Equations. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69881-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-69881-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69883-5

  • Online ISBN: 978-3-642-69881-1

  • eBook Packages: Springer Book Archive