Weak solutions of degenerated quasilinear elliptic equations of higher order.
Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.
In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential operators formed...
Weighted Sobolev and Poincaré Inequalities and Quasiregular Mappings of Polynomial Type.
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.