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Regularity of solutions to the polyharmonic equation in general domains
Regularity of solutions polyharmonic equation general domains Analysis of PDEs
2012/6/9
The present paper establishes boundedness of $[m-\frac n2+\frac 12]$ derivatives for the solutions to the polyharmonic equation of order $2m$ in arbitrary bounded open sets of $\RR^n$, $2\leq n\leq 2m...
Regularity of solutions of a free boundary problem modeling the growth of solid tumors
Free boundary problem tumor model regularity
2011/10/15
In this paper we study a free boundary problem modeling the growth of solid tumors. Due to the free boundary and surface tension effects, this problem is a nonlinear problem involving non-local terms....
Lipschitz Regularity of Solutions for Mixed Integro-Differential Equations
regularity of generalized solutions viscosity solutions nonlinear elliptic equations
2011/9/13
Abstract: We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's m...
Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations
Navier-Stokes equations nonlinear Fokker-Planck equations global existence.
2014/4/3
We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori ...