Critical points of non-regular integral functionals

  • Lucio Boccardo

    Università di Roma La Sapienza, Italy
  • Benedetta Pellacci

    Università degli Studi della Campania "Luigi Vanvitelli", Caserta, Italy
Critical points of non-regular integral functionals cover
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Abstract

We prove the existence of a bounded positive critical point for a class of functionals such as

J(v)=12o[a(x)+b(x)vγ]v2ovpJ(v)=\frac12\int_o [a(x)+b(x)|v|^{\gamma}]\, |\nabla v|^{2}-\int_o |v|^{p}

for Ω\Omega a bounded open set in RN\mathbb R^{N}, N>2N>2,γ+2<p<2N/(N2)\gamma+2< p < 2N/(N-2), γ>0\gamma>0, γ1\gamma\neq 1 and a(x),b(x)a(x),\,b(x) measurable function satisfying 0<αa(x)β0<\alpha\leq a(x)\leq \beta,0b(x)β0\leq b(x)\leq\beta almost everywhere in Ω\Omega.

Cite this article

Lucio Boccardo, Benedetta Pellacci, Critical points of non-regular integral functionals. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1001–1020

DOI 10.4171/RMI/1013