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| Format: | Artículo científico |
| Langue: | en |
| Publié: |
Universidad Industrial de Santander
2019
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| Accès en ligne: | https://www.redalyc.org/articulo.oa?id=327062425005 https://www.redalyc.org/journal/3270/327062425005/ https://www.redalyc.org/journal/3270/327062425005/html/ https://www.redalyc.org/journal/3270/327062425005/327062425005.epub https://www.redalyc.org/journal/3270/327062425005/movil |
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| _version_ | 1866574278709739520 |
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| author | Rosa Pardo |
| author_facet | Rosa Pardo |
| contents | On the existence of a priori bounds for positive solutions of elliptic problems, I Rosa Pardo Física, Astronomía y Matemáticas 35J92 35B33 35J47 35J60 35J61 This paper gives a survey over the existence of uniform L°° a priori bounds for positive solutions of subcritical elliptic equations (P)p-Apu=f(u), inu, u=0,on sobre OU widening the known ranges of subcritical nonlinearities for which positive solutions are a-priori bounded. Our arguments rely on the moving planes method, a Pohozaev identity, W 1,q regularity for q > N, and Morrey's Theorem. In this part I, when p = 2, we show that there exists a-priori bounds for classical, positive solutions of (P)2 with f (u) = u2*-1/ln(e + u)α, with 2* = 2N/(N - 2), and α > 2/(N - 2). Appealing to the Kelvin transform, we cover non-convex domains.In a forthcoming paper containing part II, we extend our results for Hamil-tonian elliptic systems (see 22), and for the p-Laplacian (see 10). We also study the asymptotic behavior of radially symmetric solutions u α = u α (r) of (P)2 as D -- 0(sec (24)). 2019 artículo científico 0120-419X https://www.redalyc.org/articulo.oa?id=327062425005 https://www.redalyc.org/journal/3270/327062425005/ https://www.redalyc.org/journal/3270/327062425005/html/ https://www.redalyc.org/journal/3270/327062425005/327062425005.epub https://www.redalyc.org/journal/3270/327062425005/movil 10.18273/revint.v37n1-2019005 en http://www.redalyc.org/revista.oa?id=3270 Revista Integración application/pdf Universidad Industrial de Santander Revista Integración (Colombia) Num.1 Vol.37 |
| format | Artículo científico |
| id | redalyc_327062425005 |
| language | en |
| publishDate | 2019 |
| publisher | Universidad Industrial de Santander |
| spellingShingle | On the existence of a priori bounds for positive solutions of elliptic problems, I Rosa Pardo Física, Astronomía y Matemáticas 35J92 35B33 35J47 35J60 35J61 On the existence of a priori bounds for positive solutions of elliptic problems, I Rosa Pardo Física, Astronomía y Matemáticas 35J92 35B33 35J47 35J60 35J61 This paper gives a survey over the existence of uniform L°° a priori bounds for positive solutions of subcritical elliptic equations (P)p-Apu=f(u), inu, u=0,on sobre OU widening the known ranges of subcritical nonlinearities for which positive solutions are a-priori bounded. Our arguments rely on the moving planes method, a Pohozaev identity, W 1,q regularity for q > N, and Morrey's Theorem. In this part I, when p = 2, we show that there exists a-priori bounds for classical, positive solutions of (P)2 with f (u) = u2*-1/ln(e + u)α, with 2* = 2N/(N - 2), and α > 2/(N - 2). Appealing to the Kelvin transform, we cover non-convex domains.In a forthcoming paper containing part II, we extend our results for Hamil-tonian elliptic systems (see 22), and for the p-Laplacian (see 10). We also study the asymptotic behavior of radially symmetric solutions u α = u α (r) of (P)2 as D -- 0(sec (24)). 2019 artículo científico 0120-419X https://www.redalyc.org/articulo.oa?id=327062425005 https://www.redalyc.org/journal/3270/327062425005/ https://www.redalyc.org/journal/3270/327062425005/html/ https://www.redalyc.org/journal/3270/327062425005/327062425005.epub https://www.redalyc.org/journal/3270/327062425005/movil 10.18273/revint.v37n1-2019005 en http://www.redalyc.org/revista.oa?id=3270 Revista Integración application/pdf Universidad Industrial de Santander Revista Integración (Colombia) Num.1 Vol.37 |
| title | On the existence of a priori bounds for positive solutions of elliptic problems, I |
| topic | Física, Astronomía y Matemáticas 35J92 35B33 35J47 35J60 35J61 |
| url | https://www.redalyc.org/articulo.oa?id=327062425005 https://www.redalyc.org/journal/3270/327062425005/ https://www.redalyc.org/journal/3270/327062425005/html/ https://www.redalyc.org/journal/3270/327062425005/327062425005.epub https://www.redalyc.org/journal/3270/327062425005/movil |