Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPrecise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data
61
0
0.0
(
0
)
Added by
Lyoubomira Softova Palagacheva
Publication date
2020
fields
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider the Dirichlet problem for a class of quasilinear elliptic systems in domain with irregular boundary. The principal part satisfies componentwise coercivity condition and the nonlinear terms are Caratheodory maps having Morrey regularity in $x$ and verifying controlled growth conditions with respect to the other variables. We have obtained boundedness of the weak solution to the problem that permits to apply an iteration procedure in order to find optimal Morrey regularity of its gradient.
rate research
Read More
We prove global essential boundedness for the weak solutions of divergence form quasilinear systems. The principal part of the differential operator is componentwise coercive and supports controlled growths with respect to the solution and its gradient, while the lower order term exhibits componentwise controlled gradient growth. The x-behaviour of the nonlinearities is governed in terms of Morrey spaces.
We show that local weak solutions to parabolic systems of p-Laplace type are H{o}lder continuous in time with values in a spatial Lebesgue space and H{o}lder continuous on almost every time line. We provide an elementary and self-contained proof building on the local higher integrability result of Kinnunen and Lewis.
This paper deals with existence and regularity of positive solutions of singular elliptic problems on a smooth bounded domain with Dirichlet boundary conditions involving the $Phi$-Laplacian operator. The proof of existence is based on a variant of the generalized Galerkin method that we developed inspired on ideas by Browder and a comparison principle. By using a kind of Moser iteration scheme we show $L^{infty}(Omega)$-regularity for positive solutions
This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of the equations, and with the help of the De Giorgi-Nash estimate for elliptic equations, we obtain existence of weak solutions on Lipschitz domains for general boundary data. Using Campanatos method, we establish regularity results of the weak solutions.
We are concerned with nonexistence results for a class of quasilinear parabolic differential problems with a potential in $Omegatimes(0,+infty)$, where $Omega$ is a bounded domain. In particular, we investigate how the behavior of the potential near the boundary of the domain and the power nonlinearity affect the nonexistence of solutions. Particular attention is devoted to the special case of the semilinear parabolic problem, for which we show that the critical rate of growth of the potential near the boundary ensuring nonexistence is sharp.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
