Symmetry and monotonicity of singular solutions of double phase problems

Biagi, Stefano; Esposito, Francesco; Vecchi, Eugenio

doi:10.1016/j.jde.2021.01.029

Cited by 26 publications

(20 citation statements)

References 42 publications

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“…-In Section 3 we show Theorem 1.6. We prove here the key Lemma 3.1 borrowing some ideas contained in [3,13,14,18]. After that, we develop a nice variant of the well-known moving plane method of Alexandrov and Serrin (see [1,25]).…”

Section: Introductionmentioning

confidence: 98%

Regularity and symmetry results for nonlinear degenerate elliptic equations

Esposito¹,

Sciunzi²,

Trombetta³

2021

Preprint

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In this paper we prove regularity results for a class of nonlinear degenerate elliptic equations of the form − div(A(|∇u|)∇u) + B (|∇u|) = f (u); in particular, we investigate the second order regularity of the solutions. As a consequence of these results, we obtain symmetry and monotonicity properties of positive solutions for this class of degenerate problems in convex symmetric domains via a suitable adaption of the celebrated moving plane method of Alexandrov-Serrin.

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Section: Introductionmentioning

confidence: 98%

Regularity and symmetry results for nonlinear degenerate elliptic equations

Esposito¹,

Sciunzi²,

Trombetta³

2021

Preprint

Self Cite

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“…Other existence results for double phase problems based on truncation and comparison techniques can be found in the papers of Fiscella [30] (Hardy potentials), Fiscella-Pinamonti [31] (Kirchhoff type problem), Gasiński-Winkert [34,35] (parametric and convection problems), Papageorgiou-Rȃdulescu-Repovš [52] (ground state solutions), Zeng-Bai-Gasiński-Winkert [62,63] (multivalued obstacle problems) and the references therein. For related works dealing with certain types of double phase problems we refer to the works of Barletta-Tornatore [5], Biagi-Esposito-Vecchi [13], Papageorgiou-Rȃdulescu-Repovš [51] and Rȃdulescu [55].…”

Section: Introductionmentioning

confidence: 99%

A new class of double phase variable exponent problems: Existence and uniqueness

Crespo-Blanco¹,

Gasiński²,

Harjulehto³

et al. 2021

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In this paper we introduce a new class of quasilinear elliptic equations driven by the so-called double phase operator with variable exponents. We prove certain properties of the corresponding Musielak-Orlicz Sobolev spaces (completeness, reflexivity, an equivalent norm) and the properties of the new double phase operator (continuity, strict monotonicity, (S + )-property). Finally we show the existence and uniqueness of corresponding elliptic equations with right-hand sides that have gradient dependence (so-called convection terms) under very general assumptions on the data. As a result of independent interest, we also show the density of smooth functions in the new Musielak-Orlicz Sobolev space even when the domain is unbounded.

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“…To the best of our knowledge, Theorem 1.1 is new and extends some of the results contained in [25,38] to the case involving first order terms. This technique is so powerful and flexible that covers also the following cases: unbounded sets [25,38], the p-Laplacian operator [26,35], double phase operators [6], cooperative elliptic systems [7,8,24], the fractional Laplacian [36] and mixed local-nonlocal elliptic operators [5].…”

Section: Introductionmentioning

confidence: 99%