Existence of solutions for Navier problems with degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro

Displaying similar documents to “Existence of solutions for Navier problems with degenerate nonlinear elliptic equations”

Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations $\begin{matrix} Δ (v (x) {| Δ u |}^{p - 2} Δ u) & - \sum_{j = 1}^{n} D_{j} [ω_{1} (x) 𝒜_{j} (x, u, \nabla u)] + b (x, u, \nabla u) ω_{2} (x) \\ = f_{0} (x) - \sum_{j = 1}^{n} D_{j} f_{j} (x), in Ω \end{matrix}$ in the setting of the weighted Sobolev spaces.

Uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2014)

Applicationes Mathematicae

Similarity:

We investigate the existence and uniqueness of solutions to the Dirichlet problem for a degenerate nonlinear elliptic equation $- \sum_{i, j = 1}^{n} D_{j} (a_{i j} (x) D_{i} u (x)) + b (x) u (x) + d i v (Φ (u (x))) = g (x) - \sum_{j = 1}^{n} f_{j} (x)$ on Ω in the setting of the space H₀(Ω).

Solvability of the stationary Stokes system in spaces $H ²_{- μ}$ , μ ∈ (0,1)

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

Similarity:

We consider the stationary Stokes system with slip boundary conditions in a bounded domain. Assuming that data functions belong to weighted Sobolev spaces with weights equal to some power of the distance to some distinguished axis, we prove the existence of solutions to the problem in appropriate weighted Sobolev spaces.

On the regular solutions for some classes of Navier-Stokes equations

Y. Ebihara, L.A. Medeiros (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Similarity:

Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity

K. Pileckas (1997)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity

S. A. Nazarov, K. Pileckas (1998)

Rendiconti del Seminario Matematico della Università di Padova

Similarity:

Existence of solutions to the nonstationary Stokes system in $H_{- μ}^{2, 1}$ , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

W. M. Zajączkowski (2007)

Applicationes Mathematicae

Similarity:

We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the...

Elliptic regularization and Navier-Stokes system.

Adauto Medeiros, Luis, Limaco Ferrel, Juan (1997)

Memoirs on Differential Equations and Mathematical Physics

Similarity:

On positive solutions of quasilinear elliptic systems

Yuanji Cheng (1997)

Czechoslovak Mathematical Journal

Similarity:

In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems $\}\begin{matrix} - Δ_{p} u = f (x, u, v), & in Ω, - Δ_{p} v = g (x, u, v), & in Ω, u = v = 0, & on \partial Ω, \end{matrix}$ where $- Δ_{p}$ is the $p$ -Laplace operator, $p > 1$ and $Ω$ is a $C^{1, α}$ -domain in $ℝ^{n}$ . We prove an analogue of [7, 16] for the eigenvalue problem with $f (x, u, v) = λ_{1} v^{p - 1}$ , $g (x, u, v) = λ_{2} u^{p - 1}$ and obtain a non-existence result of positive solutions for the general systems.