The extremal solution for the fractional Laplacian

We study the extremal solution for the problem ( - Δ ) s u = λ f ( u ) in Ω , u ≡ 0 in R n ∖ Ω , where λ > 0 is a parameter and s ∈ ( 0 , 1 ) . We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities w...

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Bibliographic Details
Published in:	Calculus of variations and partial differential equations Vol. 50; no. 3-4; pp. 723 - 750
Main Authors:	Ros-Oton, Xavier, Serra, Joaquim
Format:	Journal Article Publication
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2014 Springer Nature B.V
Subjects:	Analysis Applied mathematics Boundaries BOUNDEDNESS Calculus of variations Calculus of variations and optimal control Calculus of Variations and Optimal Control; Optimization Control Càlcul de variacions DIMENSION 4 Estimates INEQUALITIES Matemàtica aplicada a les ciències Matemàtiques i estadística Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Maximum principle MINIMIZERS Nonlinearity OPERATORS Optimization Partial differential equations POSITIVE SOLUTIONS REGULARITY SEMILINEAR ELLIPTIC-EQUATIONS Symmetry Systems Theory Texts Theoretical VARIATIONAL-METHODS Àrees temàtiques de la UPC 35R11 Secondary 35B45 35R09 Primary 35J61 35B35
ISSN:	0944-2669, 1432-0835
Online Access:	Get full text
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