On a generalized heat potential
On a theorem of Cartan
On coincidence of p-module of a family of curves and p-capacity on the Carnot group.
The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. In particular, the coincidence of the p-module and the p-capacity plays an mportant role. We consider this problem on the Carnot group. The Carnot group G is a simply connected nilpotent Lie group equipped vith an appropriate family of dilations. Let omega be a bounded domain on G and Ko, K1 be disjoint non-empty...
On -solutions of the Laplace equation and zeros of holomorphic functions
On Liouville type theorems for second order elliptic differential equations
On ordinary differentiability of Bessel potentials
On the -Laplacian.
On the base and the essential base in parabolic potential theory
On the boundedness and compactness of generalized truncated potentials.
On the continuity of strongly nonlinear potential
On the dimension of -harmonic measure in space
Let , and let , be given. In this paper we study the dimension of -harmonic measures that arise from non-negative solutions to the -Laplace equation, vanishing on a portion of , in the setting of -Reifenberg flat domains. We prove, for , that there exists small such that if is a -Reifenberg flat domain with , then -harmonic measure is concentrated on a set of -finite -measure. We prove, for , that for sufficiently flat Wolff snowflakes the Hausdorff dimension of -harmonic measure...
On the existence of weighted boundary limits of harmonic functions
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
On the heat potential of the double distribution
On the instability of Hausdorff content.
On the -boundedness of nonisotropic spherical Riesz potentials.
Orlicz-Sobolev spaces with zero boundary values on metric spaces.