For fully nonlinear nonlocal concave or convex elliptic operators I with f in L^infty(B1), the equation Iu = f in B1 implies u in C^{2s}(B_{1/2}).
Fractional thoughts
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
In this note we present some of the most basic aspects of the fractional Laplacean with a self-contained and purely didactic intent, and with a somewhat different slant from the several excellent existing references. Given the interest that nonlocal operators have generated since the 2007 extension paper of Caffarelli and Silvestre, we feel it is appropriate offering to young researchers a quick additional guide to the subject which, we hope, will nicely complement the existing ones.
fields
math.AP 3verdicts
UNVERDICTED 3representative citing papers
As s approaches 0+, s-harmonic functions u_s have asymptotics and s-derivatives expressible via the logarithmic Laplacian of extensions of the exterior data g, yielding pointwise monotonicity in s for many g.
Improved global and local Gagliardo-Nirenberg inequalities with BMO terms are obtained by using fractional Laplacians in place of local derivatives.
citing papers explorer
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$C^{2s}$ regularity for fully nonlinear nonlocal equations with bounded right hand side
For fully nonlinear nonlocal concave or convex elliptic operators I with f in L^infty(B1), the equation Iu = f in B1 implies u in C^{2s}(B_{1/2}).
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$s$-harmonic functions in the small order limit
As s approaches 0+, s-harmonic functions u_s have asymptotics and s-derivatives expressible via the logarithmic Laplacian of extensions of the exterior data g, yielding pointwise monotonicity in s for many g.
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Gagliardo-Nirenberg type inequalities with a BMO term and fractional Laplacians
Improved global and local Gagliardo-Nirenberg inequalities with BMO terms are obtained by using fractional Laplacians in place of local derivatives.