András Domokos

Subelliptic Cordes estimates

We prove Cordes type estimates for subelliptic linear partial differential operators in non-divergence form with measurable coefficients in the Heisenberg group. As an application we establish interior horizontal W 2,2- regularity for p-harmonic functions in the Heisenberg group H 1 for the range 17-1 2 ≤ p < 5+5 2.

NEARNESS, ACCRETIVITY, AND THE SOLVABILITY OF NONLINEAR EQUATIONS

In this paper our propose is to find a common term which is included in the assumptions of theorems proving existence of zeros, implicit functions, fixed points or coincidence points. This new point of view allows us to weaken the assumptions which guarantee the solvability of nonlinear equations and to recommend a possible unified treatment of several classes of operators which appear in the theory of nonlinear equations.

On the best constant for the Friedrichs-Knapp-Stein inequality in free nilpotent Lie groups of step two and applications to subelliptic PDE

In this article we propose to find the best constant for the Friedrichs-Knapp-Stein inequality in F2n,2, that is the free nilpotent Lie group of step two on 2n generators, and to prove the second-order differentiability of subelliptic p-harmonic functions in an interval of p.