A nonlocal isoperimetric problem with density perimeter
| Autor: | Lia Bronsard, Andres Zuniga, Stan Alama, Ihsan Topaloglu |
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| Přispěvatelé: | Department of Mathematics and Statistics [Hamilton], McMaster University [Hamilton, Ontario], Virginia Commonwealth University (VCU), Instituto de Ciencias de la Ingenieria (ICIn - UOH), Universidad de O'Higgins (UOH), ZUNIGA, Andres |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Monomial
49Q10 49Q20 49J10 28A75 Applied Mathematics 010102 general mathematics [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] Type (model theory) 01 natural sciences [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA] 010101 applied mathematics Combinatorics Mathematics - Analysis of PDEs Bounded function FOS: Mathematics Exponent [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Ball (mathematics) Limit (mathematics) 0101 mathematics Isoperimetric inequality [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP] Analysis Analysis of PDEs (math.AP) Energy functional Mathematics |
| Popis: | We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is controlled by a parameter $\gamma$. We show that for a wide class of density functions the energy admits a minimizer for any value of $\gamma$. Moreover these minimizers are bounded. For monomial densities of the form $|x|^p$ we prove that when $\gamma$ is sufficiently small the unique minimizer is given by the ball of fixed volume. In contrast with the constant density case, here the $\gamma\to 0$ limit corresponds, under a suitable rescaling, to a small mass $m=|\Omega|\to 0$ limit when $pd-\alpha+1$. Comment: This version will appear in Calc. Var. Partial Differential Equations |
| Databáze: | OpenAIRE |
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