Abstract:
In this paper we consider classical solutions u of the semilinear fractional problem (- Δ) su= f(u) in R+N with u= 0 in RN\\R+N, where (- Δ) s, 0 < s< 1 , stands for the fractional laplacian, N≥ 2 , R+N={x=(x′,xN)∈RN:xN>0} is the half-space and f∈ C1 is a given function. With no additional restriction on the function f, we show that bounded, nonnegative, nontrivial classical solutions are indeed positive in R+N and verify (Formula presented.). This is in contrast with previously known results for the local case s= 1 , where nonnegative solutions which are not positive do exist and the monotonicity property above is not known to hold in general even for positive solutions when f(0) < 0. © 2017, Springer-Verlag Berlin Heidelberg.
Registro:
Documento: |
Artículo
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Título: | Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
Autor: | Barrios, B.; Del Pezzo, L.; García-Melián, J.; Quaas, A. |
Filiación: | Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, La Laguna, 38200, Spain Departamento de Matemática FCEyN, UBA, CONICET, Ciudad Universitaria Pab I, Buenos Aires, 1428, Argentina Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y Fotónica, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, La Laguna, 38200, Spain Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla V-110, Avda. España, 1680, Valparaiso, Chile
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Palabras clave: | 35S15; 45M20; 47G10 |
Año: | 2017
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Volumen: | 56
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Número: | 2
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DOI: |
http://dx.doi.org/10.1007/s00526-017-1133-9 |
Título revista: | Calculus of Variations and Partial Differential Equations
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Título revista abreviado: | Calc. Var. Partial Differ. Equ.
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ISSN: | 09442669
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v56_n2_p_Barrios |
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Citas:
---------- APA ----------
Barrios, B., Del Pezzo, L., García-Melián, J. & Quaas, A.
(2017)
. Monotonicity of solutions for some nonlocal elliptic problems in half-spaces. Calculus of Variations and Partial Differential Equations, 56(2).
http://dx.doi.org/10.1007/s00526-017-1133-9---------- CHICAGO ----------
Barrios, B., Del Pezzo, L., García-Melián, J., Quaas, A.
"Monotonicity of solutions for some nonlocal elliptic problems in half-spaces"
. Calculus of Variations and Partial Differential Equations 56, no. 2
(2017).
http://dx.doi.org/10.1007/s00526-017-1133-9---------- MLA ----------
Barrios, B., Del Pezzo, L., García-Melián, J., Quaas, A.
"Monotonicity of solutions for some nonlocal elliptic problems in half-spaces"
. Calculus of Variations and Partial Differential Equations, vol. 56, no. 2, 2017.
http://dx.doi.org/10.1007/s00526-017-1133-9---------- VANCOUVER ----------
Barrios, B., Del Pezzo, L., García-Melián, J., Quaas, A. Monotonicity of solutions for some nonlocal elliptic problems in half-spaces. Calc. Var. Partial Differ. Equ. 2017;56(2).
http://dx.doi.org/10.1007/s00526-017-1133-9