Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
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...
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todo:paper_09442669_v56_n2_p_Barrios2023-10-03T15:49:13Z Monotonicity of solutions for some nonlocal elliptic problems in half-spaces Barrios, B. Del Pezzo, L. García-Melián, J. Quaas, A. 35S15 45M20 47G10 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. Fil:Del Pezzo, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09442669_v56_n2_p_Barrios |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
35S15 45M20 47G10 |
| spellingShingle |
35S15 45M20 47G10 Barrios, B. Del Pezzo, L. García-Melián, J. Quaas, A. Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| topic_facet |
35S15 45M20 47G10 |
| description |
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. |
| format |
JOUR |
| author |
Barrios, B. Del Pezzo, L. García-Melián, J. Quaas, A. |
| author_facet |
Barrios, B. Del Pezzo, L. García-Melián, J. Quaas, A. |
| author_sort |
Barrios, B. |
| title |
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| title_short |
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| title_full |
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| title_fullStr |
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| title_full_unstemmed |
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| title_sort |
monotonicity of solutions for some nonlocal elliptic problems in half-spaces |
| url |
http://hdl.handle.net/20.500.12110/paper_09442669_v56_n2_p_Barrios |
| work_keys_str_mv |
AT barriosb monotonicityofsolutionsforsomenonlocalellipticproblemsinhalfspaces AT delpezzol monotonicityofsolutionsforsomenonlocalellipticproblemsinhalfspaces AT garciamelianj monotonicityofsolutionsforsomenonlocalellipticproblemsinhalfspaces AT quaasa monotonicityofsolutionsforsomenonlocalellipticproblemsinhalfspaces |
| _version_ |
1807317351915323392 |