arXiv subjects

Matthieu Felsinger

Publications and source records attributed to Matthieu Felsinger.

2 recordsLinked to original sources

arXiv2013

The Dirichlet problem for nonlocal operators

In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a given bounded set. We formulate the problem in the classical framework of Hilbert spaces and prove unique solvability using standard techniques like the Fredholm alternative.

math.AP↗

arXiv2013

Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $α\in (α_0, 2)$ are studied. Local a priori estimates of Hölder norms and a weak Harnack inequality are proved. These results are robust with respect to $α\nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.

math.AP↗