We give sufficient conditions for the existence of solutions of the minimum problem $$ {cal P}_{u_0}: qquad hbox{Minimize}quad int_Omega g(Du(x))dx, quad uin u_0 + W_0^{1,p}(Omega,{Bbb R}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0in W_0^{1,p}(Omega,{Bbb R})$.

Minimization of the functional of the gradient by Baire's theorem / Zagatti, Sandro. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 38:2(2000), pp. 384-399. [10.1137/S0363012998335206]

Minimization of the functional of the gradient by Baire's theorem

Zagatti, Sandro
2000-01-01

Abstract

We give sufficient conditions for the existence of solutions of the minimum problem $$ {cal P}_{u_0}: qquad hbox{Minimize}quad int_Omega g(Du(x))dx, quad uin u_0 + W_0^{1,p}(Omega,{Bbb R}), $$ based on the structure of the epigraph of the lower convex envelope of g, which is assumed be lower semicontinuous and to grow at infinity faster than the power p with p larger than the dimension of the space. No convexity conditions are required on g, and no assumptions are made on the boundary datum $u_0in W_0^{1,p}(Omega,{Bbb R})$.
2000
38
2
384
399
https://epubs.siam.org/doi/10.1137/S0363012998335206
Zagatti, Sandro
File in questo prodotto:
File Dimensione Formato  
SJC000384.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 361.7 kB
Formato Adobe PDF
361.7 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: https://hdl.handle.net/20.500.11767/13204
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 20
  • ???jsp.display-item.citation.isi??? 17
social impact