C¹(Rᴺ) Versus W¹,ᵖ(Rᴺ) Local Minimizers

Authors

  • Dumitru Motreanu University of Perpignan, Department of Mathematics, 66860 Perpignan, France

DOI:

https://doi.org/10.37256/cm.3220221358

Keywords:

quasilinear elliptic equation in Rᴺ, p-Laplacian, energy functional, local minimizer, Sobolev spaces

Abstract

This paper deals with the energy functional associated with a quasilinear elliptic equation in RN which is driven by the p-Laplacian operator. It is shown for such functional that any C1(RN) local minimizer in an appropriate sense is a W1,p(RN) local minimizer. This extends to RN the celebrated property of Brezis-Nirenberg type known for bounded domains.

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Published

2022-06-09

How to Cite

1.
Motreanu D. C¹(Rᴺ) Versus W¹,ᵖ(Rᴺ) Local Minimizers. Contemp. Math. [Internet]. 2022 Jun. 9 [cited 2024 Mar. 4];3(2):232-41. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1358