We are concerned with positive solutions of the fractional elliptic system () where Ω is an arbitrary domain in (), and , for some . We establish universal a priori estimate for positive solutions of (E). Then for bounded ...

In this dissertation we present a brief introduction to theory of elliptic partial differential equations (PDE). First we review theory of Sobolev spaces. After that we discuss existence, regularity and other qualitative ...

Under the lack of variational structure and nondegeneracy, we investigate three notions of generalized principal eigenvalue for a general infinity Laplacian operator with gradient and homogeneous term. A Harnack inequality ...