A symmetrization result for elliptic equations with lower-order terms

Trombetti, Guido; Vázquez, Juan Luís

doi:10.5802/afst.619

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Introduction2

Proposition 32 Assume (I)-(vi) Hold and D I (X T) ≡ 0 Let1

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2003

2022

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Cited by 29 publications

(23 citation statements)

References 4 publications

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“…Under the assumptions of Proposition 3.2, as is bounded, using Schwarz symmetrization, some comparison results for elliptic equations have been obtained in [28]. However, as is unbounded, there are no comparison results for elliptic and parabolic equations under the same assumptions up to now.…”

Section: Proposition 32 Assume (I)-(vi) Hold and D I (X T) ≡ 0 Letmentioning

confidence: 93%

On the Case of Equalities in Comparison Results for Parabolic Equations Related to Gauss Measure

2011

Potential Anal

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Section: Proposition 32 Assume (I)-(vi) Hold and D I (X T) ≡ 0 Letmentioning

confidence: 93%

On the Case of Equalities in Comparison Results for Parabolic Equations Related to Gauss Measure

2011

Potential Anal

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“…Our result (1.8) gives a comparison result with the problem (1.7) that is closer to the starting one (1.1). Results of this type can be found in [6], [9], [17].…”

Section: Introductionmentioning

confidence: 99%

Comparison results for nonlinear elliptic equations with lower–order terms

Ferone

Messano

2003

Mathematische Nachrichten

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We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A(u) + g(x, u) = f , where the principal term is a Leray-Lions operator defined on W 1,p 0 (Ω) and g(x, u) is a term having the same sign as u and satisfying suitable growth assumptions. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.

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“…This kind of results is now classic since the papers by Talenti [27,28] where Schwarz symmetrization is used to treat the linear case. Anyway, this technique works well when the nonlinearity is an increasing function of u (see for instance [3,7,8,16,17,25,29]). To our knowledge the only paper that deals with the decreasing nonlinearity u −γ , γ > 0, is [12], where the equation − u = f /u γ is considered.…”

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confidence: 97%