-regularity of the Aronsson equation in
We prove the Hölder continuity of the homogeneous gradient of the weak solutions of the p-Laplacian on the Heisenberg group , for .
We prove the equivalence of various capacitary strong type estimates. Some of them appear in the characterization of the measures that are admissible data for the existence of solutions to semilinear elliptic problems with power growth. Other estimates are known to characterize the measures for which the Sobolev space can be imbedded into . The motivation comes from the semilinear problems: simpler descriptions of admissible data are given. The proof surprisingly involves the theory of singular...
We establish the existence of a capacity solution for a degenerate anisotropic stationary system with variable exponents and electrical conductivity. The system is a generalization of the thermistor problem, addressing the interaction between temperature and electric potential within semiconductor material.
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...