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We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation of prescribed horizontal Gauss curvature in a Carnot group.
We characterize when radial weak solutions to Monge-Ampere equations are smooth. This paper extends previous partial results and also covers Generalized Monge-Ampere equations and infinitely vanishing right hand side.
We find normal forms for parabolic Monge-Ampere equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case,
We revisit the paper [Mel86] by R. Melrose, providing a full proof of the main theorem on propagation of singularities for subelliptic wave equations, and linking this result with sub-Riemannian geometry. This result asserts that singularities of sub
We prove that integrability of a dispersionless Hirota type equation implies the symplectic Monge-Ampere property in any dimension $geq 4$. In 4D this yields a complete classification of integrable dispersionless PDEs of Hirota type through a list of
We prove that generalised Monge-Ampere equations (a family of equations which includes the inverse Hessian equations like the J-equation, as well as the Monge-Ampere equation) on projective manifolds have smooth solutions if certain intersection numb