A priori estimates for solutions to anisotropic elliptic problems via symmetrization

Alberico, Angela; Blasio, Giuseppina di; Feo, Filomena

doi:10.1002/mana.201500282

Cited by 11 publications

(11 citation statements)

References 33 publications

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“…The growing interest has led to an extensive investigation also for problems governed by fully anisotropic grows condition (see e.g. [A,AC,AdBF1,C1,C2]) and problems related to different type of anisotropy (see e.g. [AFTL,BFK,DdB2,DG]).…”

Section: Introductionmentioning

confidence: 99%

Comparison results for nonlinear anisotropic parabolic problems

Alberico¹,

Blasio²,

Feo³

2017

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semi-discretization method in time after providing estimates for solutions to anisotropic elliptic problems with zero-order terms. * Istituto per le Applicazioni del Calcolo "M. Picone", Sez. Napoli, Consiglio Nazionale delle Ricerche (CNR)

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Section: Introductionmentioning

confidence: 99%

Comparison results for nonlinear anisotropic parabolic problems

Alberico¹,

Blasio²,

Feo³

2017

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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“…The growing interest has led to an extensive investigation also for problems governed by fully anisotropic growth conditions (see [AC,A,AdBF1,C1,C3]) and problems related to different type of anisotropy (see e.g. [AFTL, BFK, DdB, DG]).…”

Section: Introductionmentioning

confidence: 99%

A Symmetrization Result for a Class of Anisotropic Elliptic Problems

2017

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“…The literature on elliptic equations, under such a broad ellipticity condition as that defined in terms of N -functions Φ, is quite limited -see e.g. [Al,AdiBF1,AdiBF2,AlCi,Ci3,GSZ,GWWZ,GSZ]. Our results answer some questions in their general theory, and provide a unified framework for results available for functions Φ of special forms.…”

Section: Introductionmentioning

confidence: 63%

Fully anisotropic elliptic problems with minimally integrable data

et al. 2019

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We investigate nonlinear elliptic Dirichlet problems whose growth is driven by a general anisotropic N -function, which is not necessarily of power type and need not satisfy the ∆2 nor the ∇2condition. Fully anisotropic, non-reflexive Orlicz-Sobolev spaces provide a natural functional framework associated with these problems. Minimal integrability assumptions are detected on the datum on the right-hand side of the equation ensuring existence and uniqueness of weak solutions. When merely integrable, or even measure, data are allowed, existence of suitably further generalized solutionsin the approximable sense -is established. Their maximal regularity in Marcinkiewicz-type spaces is exhibited as well. Uniqueness of approximable solutions is also proved in case of L 1 -data.

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A priori estimates for solutions to anisotropic elliptic problems via symmetrization

Abstract: We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

Cited by 11 publications

References 33 publications

Comparison results for nonlinear anisotropic parabolic problems

Comparison results for nonlinear anisotropic parabolic problems

A Symmetrization Result for a Class of Anisotropic Elliptic Problems

Fully anisotropic elliptic problems with minimally integrable data

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