237 research outputs found
Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings
A study of regularity estimate for weak solution to generalized stationary
Stokes-type systems involving -Laplacian is offered. The governing systems
of equations are based on steady incompressible flow of a Newtonian fluids.
This paper also provides a relatively complete picture of our main results in
two regards: problems with nonlinearity is regular with respect to the gradient
variable; and asymtotically regular problems, whose nonlinearity satisfies a
particular structure near infinity. For such Stokes-type systems, we derive
regularity estimates for both velocity gradient and its associated pressure in
two special classes of function spaces: the generalized Lorentz and
-generalized Morrey spaces.Comment: 35 page
Regularity of the extremal solution for singular p-Laplace equations
We study the regularity of the extremal solution to the singular
reaction-diffusion problem in , on
, where , , is a smooth bounded domain and is any positive, superlinear,
increasing and (asymptotically) convex nonlinearity. We provide a simple
proof of known and \textit{a priori} estimates for , i.e.
if , if and if
Partial Regularity Results for Asymptotic Quasiconvex Functionals with General Growth
We prove partial regularity for minimizers of vectorial integrals of the
Calculus of Variations, with general growth condition, imposing quasiconvexity
assumptions only in an asymptotic sense
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