Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian
| dc.creator | Aldo Henrique de Souza Medeiros | |
| dc.date.accessioned | 2019-11-04T15:09:39Z | |
| dc.date.accessioned | 2025-09-08T23:42:36Z | |
| dc.date.available | 2019-11-04T15:09:39Z | |
| dc.date.issued | 2019-08-23 | |
| dc.description.sponsorship | CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico | |
| dc.identifier.uri | https://hdl.handle.net/1843/30804 | |
| dc.language | eng | |
| dc.publisher | Universidade Federal de Minas Gerais | |
| dc.rights | Acesso Aberto | |
| dc.subject.other | Laplacian | |
| dc.subject.other | Differential equation | |
| dc.title | Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian | |
| dc.type | Tese de doutorado | |
| local.contributor.advisor1 | Emerson Alves Mendonça de Abreu | |
| local.contributor.advisor1Lattes | http://lattes.cnpq.br/0989407026771712 | |
| local.creator.Lattes | http://lattes.cnpq.br/2515109720775692 | |
| local.description.resumo | In the first part of this work, we study the regularity of weak solutions (in an appropriate space) of the elliptic partial differential equation (−∆p)su + (−∆q)su = f(x) in RN, where 0 < s < 1 and 2 ≤ q ≤ p < N/s, and we prove that these solutions are locally in C0,α(RN). In the sequence, we prove the existence of solutions of the problem (−∆p)su + (−∆q)su = |u|p∗ s−2u + λg(x)|u|r−2u in RN, where 1 < q ≤ p < N/s, λ is a parameter and g satisfies some integrability conditions. As an application of the previus result, we show that, if 0 < s < 1, 2 ≤ q ≤ p < N/s and g is bounded, then the obtained solutions are continuous and bounded. In the final part of the work, we study the behavior as p →∞ of up, a positive least energy solution of the problem h(−∆p)α +−∆q(p) βiu = µpkukp−2 ∞ u(xu)δxu in Ω u = 0 in RN \Ω |u(xu)| = kuk∞, where Ω ⊂RN is a smooth bounded domain, δxu is the Dirac delta distribution supported at xu, lim p→∞ q(p) p = Q ∈((0,1) if 0 < β < α < 1 (1,∞) if 0 < α < β < 1 and lim p→∞ p √µp > R−α, with R denoting the inradius of Ω. | |
| local.publisher.country | Brasil | |
| local.publisher.initials | UFMG | |
| local.publisher.program | Programa de Pós-Graduação em Matemática |