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Global higher integrability of solutions to subelliptic double obstacle problems. (English) Zbl 1456.35093

Summary: In this paper we consider the double obstacle problems associated with nonlinear subelliptic equation \[X^*A(x,u,Xu)+ B(x,u,Xu)=0, \quad x\in\Omega,\] where \(X=(X_1,\ldots,X_m)\) is a system of smooth vector fields defined in \(\mathbb{R}^n\) satisfying Hörmander’s condition. The global higher integrability for the gradients of the solutions is obtained under a capacitary assumption on the complement of the domain \(\Omega \).

MSC:

35H20 Subelliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35J20 Variational methods for second-order elliptic equations
35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
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