Results 41 to 50 of about 367 (79)

Up-to-Boundary Pointwise Gradient Estimates for Very Singular Quasilinear Elliptic Equations with Mixed Data

Advanced Nonlinear Studies, 2021
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed ...
Do Tan Duc, Truong Le Xuan, Trong Nguyen Ngoc   +2 more
doaj   +1 more source

On semilinear elliptic equations with borderline Hardy potentials [PDF]

, 2012
In this paper we study the asymptotic behavior of solutions to an elliptic equation near the singularity of an inverse square potential with a coefficient related to the best constant for the Hardy inequality.
Felli, Veronica, Ferrero, Alberto
core  

Analysis of a turbulence model related to that of k-epsilon for stationary and compressible flows [PDF]

, 2010
We shall study a turbulence model arising in compressible fluid mechanics. The model called $\theta - \phi$ we study is closely related to the k-epsilon model.
Dreyfuss, Pierre
core   +2 more sources

Neumann problem with a discontinuous nonlinearity

Demonstratio Mathematica
This study is devoted to proving the existence of weak solutions for a nonlinear elliptic problem with Neumann-type boundary data. The problem is driven by a discontinuous power nonlinearity and a nonsmooth prescribed data. Additionally, we aim to derive
Choudhuri Debajyoti, Repovš Dušan D., Saoudi Kamel   +2 more
doaj   +1 more source

Multiplicity of k-convex solutions for a singular k-Hessian system

Demonstratio Mathematica
In this article, we study the following nonlinear kk-Hessian system with singular weights Sk1k(σ(D2u1))=λb(∣x∣)f(−u1,−u2),inΩ,Sk1k(σ(D2u2))=λh(∣x∣)g(−u1,−u2),inΩ,u1=u2=0,on∂Ω,\left\{\begin{array}{ll}{S}_{k}^{\frac{1}{k}}(\sigma ({D}^{2}{u}_{1}))=\lambda ...
Yang Zedong, Bai Zhanbing
doaj   +1 more source

The trace space of anisotropic least gradient functions depends on the anisotropy. [PDF]

Math Ann, 2023
Górny W.
europepmc   +1 more source

Nondegeneracy of positive solutions to nonlinear Hardy–Sobolev equations

Advances in Nonlinear Analysis, 2017
In this note, we prove that the kernel of the linearized equation around a positive energy solution in ℝn${\mathbb{R}^{n}}$, n≥3${n\geq 3}$, to the problem -Δ⁢W-γ⁢|x|-2⁢V=|x|-s⁢W2⋆⁢(s)-1$-\Delta W-\gamma|x|^{-2}V=|x|^{-s}W^{2^{\star}(s)-1}$ is one ...
Robert Frédéric
doaj   +1 more source

Elliptic Equations with Hardy Potential and Gradient-Dependent Nonlinearity

Advanced Nonlinear Studies, 2020
Let Ω⊂ℝN{\Omega\subset\mathbb{R}^{N}} (N≥3{N\geq 3}) be a C2{C^{2}} bounded domain, and let δ be the distance to ∂⁡Ω{\partial\Omega}. We study equations (E±){(E_{\pm})}, -Lμ⁢u±g⁢(u,|∇⁡u|)=0{-L_{\mu}u\pm g(u,\lvert\nabla u\rvert)=0} in Ω, where Lμ=Δ+μδ2 ...
Gkikas Konstantinos T., Nguyen Phuoc-Tai
doaj   +1 more source

Dirichlet problems for fully nonlinear equations with ”subquadratic” HamiltoniansMathematical Subject Classification : 35J70, 35J75

, 2019
For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of suitably defined viscosity solution of Dirichlet problem and we further show that it is a Lipschitz continuous ...
Birindelli, Isabeau, Demengel, Françoise, Leoni, Fabiana   +2 more
openaire   +1 more source

Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Advances in Nonlinear Analysis, 2014
In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problem -Δℍnu=μg(ξ)u(|z|4+t2)12+λf(ξ,u)$-\Delta _{{\mathbb {H}}^{n}} u= \mu \frac{g(\xi ) u}{(|z|^{4}+ t^{2} )^{\frac{1}{2} }} +\lambda f(\xi , u)$ in Ω ...
Tyagi Jagmohan
doaj   +1 more source