The obstacle problem for a class of hypoelliptic ultraparabolic equations
نویسندگان
چکیده
We prove that the obstacle problem for a non-uniformly parabolic operator of Kolmogorov type, with Cauchy (or Cauchy-Dirichlet) boundary conditions, has a unique strong solution u. We also show that u is a solution in the viscosity sense.
منابع مشابه
Regularity near the Initial State in the Obstacle Problem for a class of Hypoelliptic Ultraparabolic Operators
This paper is devoted to a proof of regularity, near the initial state, for solutions to the Cauchy-Dirichlet and obstacle problem for a class of second order differential operators of Kolmogorov type. The approach used here is general enough to allow us to consider smooth obstacles as well as non-smooth obstacles. 2000 Mathematics Subject classification: 35R35, 35K70, 35R03, 35Q91
متن کاملPartial differential equations. -- Gaussian estimates for hypoelliptic operators via optimal control
Partial differential equations. — Gaussian estimates for hypoelliptic operators via optimal control, by UGO BOSCAIN and SERGIO POLIDORO, communicated on 11 May 2007. ABSTRACT. — We obtain Gaussian lower bounds for the fundamental solution of a class of hypoelliptic equations, by using repeatedly an invariant Harnack inequality. Our main result is given in terms of the value function of a suitab...
متن کاملA Gaussian upper bound for the fundamental solutions of a class of ultraparabolic equations ✩
We prove Gaussian estimates from above of the fundamental solutions to a class of ultraparabolic equations. These estimates are independent of the modulus of continuity of the coefficients and generalize the classical upper bounds by Aronson for uniformly parabolic equations. 2003 Elsevier Science (USA). All rights reserved.
متن کاملOn a class of degenerate parabolic equations of Kolmogorov type
We adapt the Levi’s parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
متن کاملPropagation of Gevrey Regularity for a Class of Hypoelliptic Equations
We prove results on the propagation of Gevrey and analytic wave front sets for a class of C∞ hypoelliptic equations with double characteristics.
متن کامل