The ε-ε property and the boundedness of isoperimetric sets with different monomial weights

Autor:	Emerson Abreu, Leandro G. Fernandes, Joel Ramirez
Rok vydání:	2023
Předmět:	Computational Mathematics Control and Optimization Control and Systems Engineering
Zdroj:	ESAIM: Control, Optimisation and Calculus of Variations. 29:28
ISSN:	1262-3377 1292-8119
DOI:	10.1051/cocv/2023023
Popis:	We consider a class of monomial weights 𝑥A = |𝑥1|𝑎1…|𝑥N|𝑎N in ℝN, where ai is a nonnegative real number for each i ∈ {1,…,N}, and we establish the ε — ε property and the boundedness of isoperimetric sets with different monomial weights for the perimeter and volume. Moreover, we present cases of nonexistence of the isoperimetric inequality when it is not possible to associate the corresponding Sobolev inequality. Finally, for N = 2, we developed an original type of symmetrization, which we call star-shaped Steiner symmetrization, and we apply it to a class of isoperimetric problems with different monomial weights.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5774c8b4a9260feb31c2241adabe281b https://doi.org/10.1051/cocv/2023023 Zobrazit plný text záznamu Plný text ve formátu PDF