On renormalized solutions to elliptic inclusions with nonstandard growth

Denkowska, Anna; Gwiazda, Piotr; Kalita, Piotr

doi:10.1007/s00526-020-01893-4

Cited by 9 publications

(2 citation statements)

References 54 publications

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“…Given an interest one may expect developing our main goals further towards anisotropic or non-reflexive settings cf. [5,24,48], as well as by involving lower-order terms in (1.1) as in [47], differential inclusions as in [41], or systems of equations.…”

Section: Is An Approximable Solution From (I) If and Only If It Is A ...mentioning

confidence: 99%

Measure data elliptic problems with generalized Orlicz growth

Chlebicka¹

2022

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We study nonlinear measure data elliptic problems involving the operator of generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well as natural variants of variable exponent and double-phase spaces. Approximable and renormalized solutions are proven to exist and coincide for arbitrary measure datum and to be unique when for a class of data being diffuse with respect to a relevant nonstandard capacity. A capacitary characterization of diffuse measures is provided.

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Section: Is An Approximable Solution From (I) If and Only If It Is A ...mentioning

confidence: 99%

Measure data elliptic problems with generalized Orlicz growth

Chlebicka¹

2022

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…In [18,29,36] isotropic, separable, and reflexive Musielak-Orlicz spaces are employed and [15] concerns separable, but not reflexive Musielak-Orlicz spaces. Existence to problems that are in the same time of general growth, inhomogeneous, and fully anisotropic were studied in [9,11,12,24,25,31,35,42], but none of them provide a direct proof. Anisotropic problems with lower-order terms are less understood -we can only refer to [13,27], but they do not cover our generality of the problem.…”

Section: Introductionmentioning

confidence: 99%

A direct proof of existence of weak solutions to fully anisotropic and inhomogeneous elliptic problems

Chlebicka¹,

Karppinen²,

Liu³

2023

Preprint

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We provide a direct proof of existence and uniqueness of weak solutions to a broad family of strongly nonlinear elliptic equations with lower-order terms. The leading part of the operator satisfies general growth conditions settling the problem in the framework of fully anisotropic and inhomogeneous Musielak-Orlicz spaces generated by an N -functionNeither ∇ 2 nor ∆ 2 conditions are imposed on M . Our results cover among others problems with anisotropic polynomial, Orlicz, variable exponent, and double phase growth.

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