8Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.
Get full text

Abstract

Let Ω ⊂ RNbe a bounded smooth domain, f : Ω × R → R be a Caratheodory function with s f (x, s) ≥ 0 ∀ (x, s) ∈ Ω × R and supx ∈ Ω| f (x, s) | ≤ C (1 + | s |)pe| s |frac(N, (N - 1)), ∀ s ∈ R, for some C > 0. Consider the functional J : W1, N(Ω) → R, Ω defined asJ (u) over(=, def) frac(1, N) {norm of matrix} u {norm of matrix}W1, N (Ω)N- under(∫, Ω) F (x, u) - frac(1, q + 1) {norm of matrix} u {norm of matrix}Lq + 1 (∂ Ω)q + 1, where F (x, u) = ∫0uf (x, s) d s and q > 0. We show that if u0∈ C1(over(Ω, -)) is a local minimum of J in the C1(over(Ω, -)) topology, then it is also a local minimum of J in W1, N(Ω) topology. To cite this article: J. Giacomoni et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.

Cite

CITATION STYLE

APA

Giacomoni, J., Prashanth, S., & Sreenadh, K. (2009). W1, N versus C1 local minimizers for elliptic functionals with critical growth in RN. Comptes Rendus Mathematique, 347(5–6), 255–260. https://doi.org/10.1016/j.crma.2009.01.010

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free