We study the minimum problem for functionals of the form F(u) = integral(I) f(x,u(x), u'(x))dx, where the integrand f : I x R-d x R-d -> R is not convex in the last variable. We provide existence results in the Sobolev space W-1,W-1(I, R) analogous to the ones obtained in W-1,W-p (I, R-d) (p > 1) by a method inspired by integro-extremization and based on Euler equations. In addition, we treat functionals with nonsmooth Lagrangians and exhibit a comparison with a direct application of integro-extremality method to a class of functionals of sum type with a separate dependence on the components of the derivative u'.

Non-convex one-dimensional functionals with superlinear growth / Zagatti, Sandro. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - 35:5-6(2022), pp. 339-358.

Non-convex one-dimensional functionals with superlinear growth

Zagatti Sandro
2022

Abstract

We study the minimum problem for functionals of the form F(u) = integral(I) f(x,u(x), u'(x))dx, where the integrand f : I x R-d x R-d -> R is not convex in the last variable. We provide existence results in the Sobolev space W-1,W-1(I, R) analogous to the ones obtained in W-1,W-p (I, R-d) (p > 1) by a method inspired by integro-extremization and based on Euler equations. In addition, we treat functionals with nonsmooth Lagrangians and exhibit a comparison with a direct application of integro-extremality method to a class of functionals of sum type with a separate dependence on the components of the derivative u'.
35
5-6
339
358
Zagatti, Sandro
File in questo prodotto:
File Dimensione Formato  
die035-0506-339.pdf

non disponibili

Descrizione: pdf
Tipologia: Documento in Post-print
Licenza: Non specificato
Dimensione 326.75 kB
Formato Adobe PDF
326.75 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/126569
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact