Regular regions for parabolic and elliptic equations
Regularity and Blow up for Active Scalars
We review some recent results for a class of fluid mechanics equations called active scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss nonlocal maximum principle methods which allow to prove existence of global regular solutions for the critical dissipation. We also recall what is known about the possibility of finite time blow...
Remark on a uniqueness result for a boundary value problem of eighth-order.
Remarks on the maximum principle for nonlinear elliptic PDEs with quadratic growth conditions
Remarks on the Phragmén-Lindelöf theorem for -viscosity solutions of fully nonlinear PDEs with unbounded ingredients.
Remarks on the strong maximum principle for nonlocal operators.
Remarks relevant to classical maximum principles.