Results 51 to 60 of about 3,540 (98)

Dirichlet problem for quasi-linear elliptic equations

Electronic Journal of Differential Equations, 2002
We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x), abla u(x))+mathcal{B}(x,u(x),abla u(x))=0.
Azeddine Baalal, Nedra Belhaj Rhouma
doaj  

The regularity of weak solutions for certain n-dimensional strongly coupled parabolic systems

Advanced Nonlinear Studies, 2022
This paper is concerned with the n-dimensional strongly coupled parabolic systems with triangular form in the cylinder Ω×(0,T]\Omega \times (0,T]. We investigate L2{L}^{2} and Hölder regularity of the derivatives of weak solutions (u1,u2)\left({u}_{1},{u}
Tan Qi-Jian
doaj   +1 more source

An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

, 2014
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to
Chae, Dongho, Constantin, Peter, Wu, Jiahong   +2 more
core   +1 more source

Global smooth solution to the n-dimensional liquid crystal equations with fractional dissipation

Demonstratio Mathematica
In this article, we focus on the global regularity of n-dimensional liquid crystal equations with fractional dissipation terms (−Δ)αu{\left(-\Delta )}^{\alpha }u and (−Δ)βd{\left(-\Delta )}^{\beta }d.
Li Wei, Wu Qiongru
doaj   +1 more source

Liouville's type results for singular anisotropic operators

Analysis and Geometry in Metric Spaces
We present two Liouville-type results for solutions to anisotropic elliptic equations that have a growth of power 2 along the first ss coordinate directions and of power pp, with ...
Maria Cassanello Filippo, Bashayer Majrashi, Vincenzo Vespri   +2 more
doaj   +1 more source

Local Elliptic Regularity for the Dirichlet Fractional Laplacian

Advanced Nonlinear Studies, 2017
We prove the Wloc2⁢s,p${W_{{\mathrm{loc}}}^{2s,p}}$ local elliptic regularity of weak solutions to the Dirichlet problem associated with the fractional Laplacian on an arbitrary bounded open set of ℝN${\mathbb{R}^{N}}$. The key tool consists in analyzing
Biccari Umberto, Warma Mahamadi, Zuazua Enrique   +2 more
doaj   +1 more source

Optimal global second-order regularity and improved integrability for parabolic equations with variable growth

Advances in Nonlinear Analysis
We consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,T){Q}_{T}:= \Omega ...
Arora Rakesh, Shmarev Sergey
doaj   +1 more source

Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues

Advances in Nonlinear Analysis, 2022
We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions,
Vitolo Antonio
doaj   +1 more source

Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates

Forum of Mathematics, Sigma, 2021
We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein–Gordon and fractional Schrödinger equations.
Neal Bez, Sanghyuk Lee, Shohei Nakamura
doaj   +1 more source

Regularity of the solutions for nonlinear biharmonic equations in R^{N} [PDF]

arXiv, 2007
The purpose of this paper is to establish the regularity the weak solutions for a nonlinear biharmonic equation.
arxiv