We study the symmetry properties for solutions of elliptic systems of the type(-δ)s1u=F1(u,v),(-δ)s2v=F2(u,v), where F∈Cloc1,1(R2), s1, s2∈(0, 1) and the operator (-δ)s is the so-called fractional Laplacian. We obtain some Poincaré-type formulas for the α-harmonic extension in the half-space, that we use to prove a symmetry result both for stable and for monotone solutions.
A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian / S. Dipierro, A. Pinamonti. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 255:1(2013), pp. 85-119. [10.1016/j.jde.2013.04.001]
A geometric inequality and a symmetry result for elliptic systems involving the fractional Laplacian
S. Dipierro
;
2013
Abstract
We study the symmetry properties for solutions of elliptic systems of the type(-δ)s1u=F1(u,v),(-δ)s2v=F2(u,v), where F∈Cloc1,1(R2), s1, s2∈(0, 1) and the operator (-δ)s is the so-called fractional Laplacian. We obtain some Poincaré-type formulas for the α-harmonic extension in the half-space, that we use to prove a symmetry result both for stable and for monotone solutions.
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