Paper
Large field problem in coercive singular PDEs
Authors
Ilya Chevyrev, Massimiliano Gubinelli
Abstract
We derive a priori estimates for singular differential equations of the form where is a polynomial, is a sufficiently well-behaved function, and is an irregular distribution such that the equation is subcritical. The differential operator is either a derivative in time, in which case we interpret the equation using rough path theory, or a heat operator, in which case we interpret the equation using regularity structures. Our only assumption on is that solutions with exhibit coercivity. Our estimates are local in space and time, and independent of boundary conditions.
One of our main results is an abstract estimate that allows one to pass from a local coercivity property to a global one using scaling, for a large class of equations. This allows us to reduce the problem of deriving a priori estimates to the case when is small.