Lewy–Stampacchia’s inequality for a Leray–Lions operator with natural growth in the gradient

Mokrane, Abdellah; Murat, François

doi:10.1007/s40574-014-0004-y

Cited by 2 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This property is crucial in variational methods to show the boundedness of Palais-Smale sequences. For instance see [4,12,16,30] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms

et al. 2021

View full text Add to dashboard Cite

It is established existence of minimal W 1, loc ( )-solutions on some appropriated set for the quasilinear elliptic problemwhere f may have indefinite sign and behaves in a strongly singular way at u = 0, h has sublinear growth, λ > 0 and μ ≥ 0 are real parameters. The main results improve the classical Brézis-Oswald's result to Orlicz-Sobolev setting in the presence of stronglysingular nonlinearities as well as gradient terms. Our approach is based on a new comparison principle for W 1, loc ( )-sub and super solutions to the -Laplacian operator established here, truncation arguments, L ∞ ( ) estimates and a generalized Galerkin method.

show abstract

“…This property is crucial in variational methods to show the boundedness of Palais-Smale sequences. For instance see [4,12,16,30] and references therein.…”

Section: Introductionmentioning

confidence: 99%

A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Many authors have studied (P ) by different methods like degree theory, sub-super solutions, a priori estimates, etc. We refer, for instance, to [5,7,9,16,21,25,26,30]. Some special cases have been studied by using variational arguments and we refer, for instance, to [1,13,18,19] for the case p = 2 and [15,17] for p > 1.…”

Section: Introductionmentioning

confidence: 99%

Elliptic equations involving the $p$-Laplacian and a gradient term having natural growth

Figueiredo¹,

Gossez

Quoirin

et al. 2019

Rev. Mat. Iberoam.

View full text Add to dashboard Cite

We investigate the problemin a bounded smooth domain Ω ⊂ R N . Using a Kazdan-Kramer change of variable we reduce this problem to a quasilinear one without gradient term and therefore approachable by variational methods. In this way we come to some new and interesting problems for quasilinear elliptic equations which are motivated by the need to solve (P ). Among other results, we investigate the validity of the Ambrosetti-Rabinowitz condition according to the behavior of g and f . Existence and multiplicity results for (P ) are established in several situations.

show abstract

Lewy–Stampacchia’s inequality for a Leray–Lions operator with natural growth in the gradient

Abstract: We prove that at least one solution of the obstacle problem with a Leray-Lions operator and a perturbation with natural growth with respect to the gradient satisfies LewyStampacchia's inequality. The proof is based on the natural penalization of the obstacle problem.

Cited by 2 publications

References 7 publications

A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms

A type of Brézis–Oswald problem to $$\Phi $$-Laplacian operator with strongly-singular and gradient terms

Elliptic equations involving the $p$-Laplacian and a gradient term having natural growth

Contact Info

Product

Resources

About