Regular Variational Integrals

  • Mariano Giaquinta
  • Giuseppe Modica
  • Jiří Souček
Chapter
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / 3. Folge. A Series of Modern Surveys in Mathematics book series (MATHE3, volume 38)

Abstract

In this chapter we deal with variational integrals
$$F(u,\Omega ): = \int\limits_\Omega {f(x,u(x),Du(x))dx} $$
(1)
defined on smooth maps u:Ω ⊂ ℝ n → ℝ N , which are regular, i.e., such that
$$F({\text{u}},\Omega ) \geqslant v{H^n}({g_u}_{,\Omega })v > 0$$
for all admissible u. Our goal is to find weak minimizers in suitable classes by the direct methods of calculus of variations.

Keywords

Manifold Lime Hull Cavitation Radon 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Mariano Giaquinta
    • 1
  • Giuseppe Modica
    • 2
  • Jiří Souček
    • 3
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly
  2. 2.Dipartimento di Matematica ApplicataUniversità di FirenzeFirenzeItaly
  3. 3.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Čzech Republic

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