Related papers: Stability inequalities for one-phase cones

For the 2D incompressible Euler equations, we establish global-in-time ($t \in \mathbb{R}$) stability of vortex quadrupoles satisfying odd symmetry with respect to both axes. Specifically, if the vorticity restricted to a quadrant is…

We give a short and elementary proof of stability for strong solutions of the spatially homogeneous Landau equation with Coulomb collisions, measured in relative entropy. The argument yields an explicit differential inequality for relative…

We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…

Mixtures of near-symmetric oppositely charged components with strong attractive short range interactions exhibit ordered lamellar phases at low temperatures. In the strong segregation limit the state of these systems can be described by the…

We review recent results regarding the problem of the stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds. We shall describe techniques and methods from smooth and non-smooth geometry, the fruitful…

We study $k$-radially symmetric solutions corresponding to topological defects of charge $\frac{k}{2}$ for integer $k \neq 0$ in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions…

In this paper we extend the interior regularity results for stable solutions in [Cabr\'{e}, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] to operators with variable coefficients. We show that stable solutions to the semilinear…

We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…

We prove stability for a class of heterogeneous catalysis models in the $L_p$-setting. We consider a setting in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. Under a…

(Abridged) We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly concentrate on the study of the HD 82943 system by employing two sets of the…

The purpose of this work is to establish a quantitative and constructive stability result for a class of subcritical Gagliardo-Nirenberg-Sobolev inequalities which interpolates between the logarithmic Sobolev inequality and the standard…

We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and…

This paper is concerned with the study of regularity and stability properties of two Euler-Bernoulli beam equations with localized singular damping. Under suitable regularity assumptions on the damping coefficient, we establish Gevrey…

This paper study the two--phase problem for the forward-backward parabolic equation with diffusion function of cubic type. Existence and uniqueness for these kind of problems were obtained in literature in the case in which the phases are…

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

We consider existence and uniqueness of homogeneous solutions $ u > 0 $ to certain PDE of $p$-Laplace type, $ p $ fixed, $ n - 1 <p< \infty, n \geq 2, $ when $ u $ is a solution in $K(\alpha)\subset\mathbb{R}^n$ where \[ K (\alpha) := \{ x…

We study properties of the semilinear elliptic equation $\Delta u = 1/u$ on domains in $R^n$, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low…

The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…

We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in $\mathbb{R}^2$. The obstacle is of general polygonal shape and the impedance parameter can be variable. We establish the stability results by…

The asymptotic behavior of a one-dimensional spectral problem with periodic coefficient is addressed for high frequency modes by a method of Bloch wave homogenization. The analysis leads to a spectral problem including both microscopic and…