Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2019 |
| Tipo de documento: | Tese |
| Idioma: | eng |
| Título da fonte: | Repositório Institucional da UFMG |
| Texto Completo: | http://hdl.handle.net/1843/30804 |
Resumo: | CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico |
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Emerson Alves Mendonça de Abreuhttp://lattes.cnpq.br/0989407026771712http://lattes.cnpq.br/2515109720775692Aldo Henrique de Souza Medeiros2019-11-04T15:09:39Z2019-11-04T15:09:39Z2019-08-23http://hdl.handle.net/1843/30804CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoIn 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.engUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilLaplacianDifferential equationLocal behavior and existence of solutions for problems involving fractional (p,q)- Laplacianinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALTese_AldoHenrique_Souza Medeiros.pdfTese_AldoHenrique_Souza Medeiros.pdfapplication/pdf569506https://repositorio.ufmg.br/bitstream/1843/30804/1/Tese_AldoHenrique_Souza%20Medeiros.pdf431d8766a1606a2bb5878574156ee1aaMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82119https://repositorio.ufmg.br/bitstream/1843/30804/2/license.txt34badce4be7e31e3adb4575ae96af679MD52TEXTTese_AldoHenrique_Souza Medeiros.pdf.txtTese_AldoHenrique_Souza Medeiros.pdf.txtExtracted texttext/plain123378https://repositorio.ufmg.br/bitstream/1843/30804/3/Tese_AldoHenrique_Souza%20Medeiros.pdf.txt36b4baac7c3b3edfd63fbb194b9294b3MD531843/308042019-11-14 13:12:23.512oai:repositorio.ufmg.br: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Repositório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2019-11-14T16:12:23Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false |
| dc.title.pt_BR.fl_str_mv |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| title |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| spellingShingle |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian Aldo Henrique de Souza Medeiros Laplacian Differential equation |
| title_short |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| title_full |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| title_fullStr |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| title_full_unstemmed |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| title_sort |
Local behavior and existence of solutions for problems involving fractional (p,q)- Laplacian |
| author |
Aldo Henrique de Souza Medeiros |
| author_facet |
Aldo Henrique de Souza Medeiros |
| author_role |
author |
| dc.contributor.advisor1.fl_str_mv |
Emerson Alves Mendonça de Abreu |
| dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0989407026771712 |
| dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/2515109720775692 |
| dc.contributor.author.fl_str_mv |
Aldo Henrique de Souza Medeiros |
| contributor_str_mv |
Emerson Alves Mendonça de Abreu |
| dc.subject.por.fl_str_mv |
Laplacian Differential equation |
| topic |
Laplacian Differential equation |
| description |
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico |
| publishDate |
2019 |
| dc.date.accessioned.fl_str_mv |
2019-11-04T15:09:39Z |
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2019-11-04T15:09:39Z |
| dc.date.issued.fl_str_mv |
2019-08-23 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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publishedVersion |
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http://hdl.handle.net/1843/30804 |
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eng |
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eng |
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Universidade Federal de Minas Gerais |
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Programa de Pós-Graduação em Matemática |
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UFMG |
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Brasil |
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Universidade Federal de Minas Gerais |
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