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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

Weak Convergence Lower Semicontinuity Isoperimetric Inequality Parametric Extension Finite Mass 
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 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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