This article is concerned with an obstacle problem for nonlinear subelliptic systems of second order with VMO coefficients. It is shown, based on a modification of A-harmonic approximation argument, that the gradient of weak solution to the corresponding obstacle problem belongs to the Morrey space .
The aim of this paper is to study properties of solutions to the fractional p-subLaplace equations on the Heisenberg group. Based on the maximum principles and the generalization of the direct method of moving planes, we obtain the symmetry and monotonicity of the solutions on the whole group and the Liouville property of solutions on a half space.
In this paper, we study the degenerate parabolic systemwhere X = {X 1 , . . . , X m } is a system of smooth real vector fields satisfying Hörmander's condition and the coefficients a αβ ij are measurable functions and their skew-symmetric part can be unbounded. After proving the L 2 estimates for the weak solutions, the higher integrability is proved by establishing a reverse Hölder inequality for weak solutions.
MSC: Primary 35K65; secondary 35K40; 35B65
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