A Lewy-Stampacchia Estimate for variational inequalities in the Heisenberg group
نویسندگان
چکیده
We consider an obstacle problem in the Heisenberg group framework, and we prove that the operator on the obstacle bounds pointwise the operator on the solution. More explicitly, if ¯ u minimizes the functional Ω |∇Hn u| 2 among the functions with prescribed Dirichlet boundary condition that stay below a smooth obstacle ψ, then 0 ≤ ∆Hn ¯ u ≤ ∆Hn ψ +. Moreover, we discuss how it could be possible to generalize the previous bound to a quasilinear setting once some regularity issues for the equation divHn |∇Hn u| p−2 ∇Hn u = f are satisfied.
منابع مشابه
Vector Optimization Problems and Generalized Vector Variational-Like Inequalities
In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector vari...
متن کاملPseudoconvex Multiobjective Continuous-time Problems and Vector Variational Inequalities
In this paper, the concept of pseudoconvexity and quasiconvexity for continuous~-time functions are studied and an equivalence condition for pseudoconvexity is obtained. Moreover, under pseudoconvexity assumptions, some relationships between Minty and Stampacchia vector variational inequalities and continuous-time programming problems are presented. Finally, some characterizations of the soluti...
متن کاملSolution existence of general variational inequalities and coincidence points
In this paper, by using a simple technique, we obtain several existence results of the solutions for general variational inequalities of Stampacchia type. We also show, that the existence of a coincidence point of two mappings is equivalent to the existence of the solution of a particular general variational inequality of Stampacchia type. As applications several coincidence and fixed point res...
متن کاملVariational Inequalities and Optimization Problems
In this paper we survey the relationships between scalar and vector variational inequalities (of differential type) and the underlying optimization problem. We show that the variational inequalities of Stampacchia type can be viewed as necessary optimality conditions, while the variational inequalities of Minty type can be considered as sufficient optimality conditions. Concerning this last sta...
متن کاملThe Equilibrium Equivalent Representation for Variational Inequalities Problems with Its Application in Mixed Traffic Flows
In this paper, we first introduce the relationship between the Hartman-Stampacchia variational inequalities (VI) problems and equilibrium programming (EP), and we present EP equivalent representation for Hartman-Stampacchia VI problems. After analyze and discuss the condition for optimization of EP, and the relation with the model transformation equivalent applied in mixed traffic assignment pr...
متن کامل