1,804 research outputs found
Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems
We consider the initial boundary value problem for the p(t, x)-Laplacian
system in a bounded domain \Omega. If the initial data belongs to L^{r_0}, r_0
\geq 2, we give a global L^{r_0}({\Omega})-regularity result uniformly in t>0
that, in the particular case r_0 =\infty, implies a maximum modulus theorem.
Under the assumption p- = \inf p(t, x) > 2n/(n+r_0), we also state L^{r_0}- L^r
estimates for the solution, for r \geq r_0. Complete proofs of the results
presented here are given in the paper [F. Crispo, P. Maremonti, M. Ruzicka,
Global L^r-estimates and regularizing effect for solutions to the p(t, x)
-Laplacian systems, accepted for publication on Advances in Differential
Equations, 2017]
Anisotropic parabolic equations with variable nonlinearity
We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional p(x, t)-Laplacian. We prove theorems of existence and uniqueness of weak solutions in suitable Orlicz-Sobolev spaces, derive global and local in time L∞ bounds for the weak solutions
Singular p-Laplacian parabolic system in exterior domains: higher regularity of solutions and related properties of extinction and asymptotic behavior in time
We consider the IBVP in exterior domains for the p-Laplacian parabolic
system. We prove regularity up to the boundary, extinction properties for p \in
( 2n/(n+2) , 2n/(n+1) ) and exponential decay for p= 2n/(n+1)
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