Regular Variational Integrals

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / 3. Folge. A Series of Modern Surveys in Mathematics book series (MATHE3, volume 38)


In this chapter we deal with variational integrals
$$F(u,\Omega ): = \int\limits_\Omega {f(x,u(x),Du(x))dx} $$
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.


Weak Convergence Lower Semicontinuity Isoperimetric Inequality Parametric Extension Finite Mass 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  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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