Results 31 to 40 of about 27,119 (279)
Nonlinear Dirichlet problem for the nonlocal anisotropic operator $L_K$ [PDF]
, 2018 In this paper we study an equation driven by a nonlocal anisotropic operator with homogeneous Dirichlet boundary conditions. We find at least three non trivial solutions: one positive, one negative and one of unknown sign, using variational methods and ...
Frassu, Silvia
core +2 more sources
Anisotropic singular logistic equations [PDF]
Opuscula MathematicaWe consider a parametric Dirichlet problem driven by the anisotropic \((p,q)\)-Laplacian and a reaction with a singular term and a superdiffusive logistic perturbation.
João Pablo Pinheiro Da Silva +3 more
doaj +1 more source
An overdetermined problem for the anisotropic capacity [PDF]
, 2016 We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in $\mathbb{R}^N$, establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of W. Reichel [Arch.
Bianchini, Chiara +2 more
core +2 more sources
Boundary regularity for anisotropic minimal Lipschitz graphs
Communications in Partial Differential Equations, 2023 We prove that $m$-dimensional Lipschitz graphs in any codimension with $C^{1,α}$ boundary and anisotropic mean curvature bounded in $L^p$, $p > m$, are regular at every boundary point with density bounded above by $1/2 +σ$, provided the anisotropic energy satisfies the uniform scalar atomic condition.
De Rosa, Antonio, Resende, Reinaldo
openaire +3 more sources
Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations [PDF]
, 2015 We consider the incompressible Euler equations on ${\mathbb R}^d$, where $d \in \{ 2,3 \}$. We prove that: (a) In Lagrangian coordinates the equations are locally well-posed in spaces with fixed real-analyticity radius (more generally, a fixed Gevrey ...
Constantin, Peter +2 more
core +2 more sources
Local regularity for an anisotropic elliptic equation [PDF]
Calculus of Variations and Partial Differential Equations, 2020 AbstractWe establish the interior Hölder continuity for locally bounded solutions, and the Harnack inequality for non-negative continuous solutions to a class of anisotropic elliptic equations with bounded and measurable coefficients, whose prototype equation is $$\begin{aligned} u_{xx}+\varDelta _{q,y} u=0\quad {\text { locally in }}{\mathbb {R ...
Naian Liao +2 more
openaire +4 more sources
Nonlinear anisotropic parabolic equations in Lm
Arab Journal of Mathematical Sciences, 2014 In this paper, we give a result of regularity of weak solutions for a class of nonlinear anisotropic parabolic equations with lower-order term when the right-hand side is an Lm function, with m being ”small”.
Fares Mokhtari
doaj +1 more source
A FEM for an optimal control problem of fractional powers of elliptic operators [PDF]
, 2015 We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi ...
Antil, Harbir, Otarola, Enrique
core +1 more source
Wulff shape characterizations in overdetermined anisotropic elliptic problems [PDF]
, 2017 We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one
Bianchini, Chiara, Ciraolo, Giulio
core +2 more sources
Regularity Criterion for the Nematic Liquid Crystal Flows in Terms of Velocity
Abstract and Applied Analysis, 2014 We study the regularity criterion for the 3D nematic liquid crystal flows in the framework of anisotropic Lebesgue space. More precisely, we proved some sufficient conditions in terms of velocity or the fractional derivative of velocity in one direction.
Ruiying Wei, Zheng-an Yao, Yin Li
doaj +1 more source