Uniqueness results for optimization problems with prescribed rearrangement

Betta, M. F.; Mercalso, A.

doi:10.1007/bf00396778

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Since Nwnr N1

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2011

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Cited by 3 publications

(2 citation statements)

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“…Arguing as in Theorem 3.1 in [8], we can prove that problem (52) is the unique problem such that equality holds in (53). More precisely we have THEOREM 5.2 Let u and w the solutions of (50) and (52) respectively.…”

Section: Since Nwnr Nmentioning

confidence: 93%

A weighted isoperimetric inequality and applications to symmetrization

Betta¹,

Brock²,

Mercaldo³

et al. 1999

J Inequal Appl

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We prove an inequality ofthe form fen a(lxl)7,-(dx) _> fen a(lxl)T,_ (dx), where Q is a bounded domain in R" with smooth boundary, B is a ball centered in the origin having the same measure as f. From this we derive inequalities comparing a weighted $obolev norm of a given function with the norm ofits symmetric decreasing rearrangement. Furthermore, we use the inequality to obtain comparison results for elliptic boundary value problems.

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Section: Since Nwnr Nmentioning

confidence: 93%

A weighted isoperimetric inequality and applications to symmetrization

Betta¹,

Brock²,

Mercaldo³

et al. 1999

J Inequal Appl

View full text Add to dashboard Cite

show abstract

“…Ferone and Posteraro have extended their results to more general equations in [17]. The case of equalities in comparison results for L ∞ or L 1 norm of the solutions has been discussed in [8] for degenerate elliptic equations without lower order terms. However, by observing the proofs in the articles mentioned above, we find that it is an essential condition that the distribution functions of solutions to "symmetrized" problems are absolutely continuous.…”

Section: Introductionmentioning

confidence: 95%