2 research outputs found
Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order and
summability growth , whose model is the fractional -Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory.Comment: To appear in Math. An
A note on fractional supersolutions
We study a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order
and summability growth , whose model is the fractional -Laplacian
with measurable coefficients. We prove that the minimum of the corresponding
weak supersolutions is a weak supersolution as well