Related papers: A compactness result for an equation with Holderia…

For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any $L^2$-bounded sequence of vector fields with $L^2$-bounded rotations and $L^2$-bounded divergences as well as $L^2$-bounded tangential…

We investigate compactness and spectral properties of multiplier operators associated with the Walsh system in the spaces $L^p[0,1]$, $1<p<\infty$. Building upon previously established criteria for boundedness of Walsh multipliers, we prove…

First of all, we establish compactness of continuous mappings of the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with the Calderon type condition on $\varphi$ and, in particular, of the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$…

In this paper, the singularity formation of classical solutions for the compressible Euler equations with general pressure law is considered. The gradient blow-up of classical solutions is shown without any smallness assumption by the…

Given a compact closed four dimensional smooth Riemannian manifold, we prove existence of extremal functions for Moser-Trudinger type inequality. The method used is Blow-up analysis combined with capacity techniques.

Given two compact sets, $E$ and $F$, on the unit circle, we study the class of subharmonic functions on the unit disk which can grow at the direction of $E$ and $F$ (sets of singularities) at different rate. The main result concerns the…

This note is a commentary on the model-theoretic interpretation of Grothendieck's double limit characterization of weak relative compactness.

This paper is concerned with the multiplicity results to a class of $p$-Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by an abstract linking lemma due to Br\'{e}zis and Nirenberg. We obtain the twofold…

Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…

This paper deals with the Landesman-Lazer type problem of elliptic equations associated with homogeneous Dirichlet boundary conditions. By using some dynamical arguments we derive some new results on bifurcation from infinity and…

We perform a Bayesian analysis of probability measures for compact star equations of state using new, disjunct constraints for mass and radius. The analysis uses a simple parametrization for hybrid equations of state to investigate the…

We improve the recent result of Chae & Tadmor in [Comm. Math. Sci. 6(3) (2008) 785-789], proving a one-sided threshold condition which leads to finite-time breakdown of the Euler-Poisson equations in arbitrary dimension n.

In this paper, using blow-up analysis, we prove a quantization result for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary. Similar results for Euclidean space were obtained by…

In this paper we derive kinematic relations for quantities involving the rate of strain tensor and the Hessian of the pressure for solutions of the 3D Euler equations and the 2D Boussinesq equations. Using these kinematic relations, we…

We prove two compactness results for function spaces with finite Dirichlet energy of half-space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic…

We extend Beem's three completeness notions -- finite compactness, timelike Cauchy completeness, and Condition A -- originally defined for spacetimes, to Lorentzian length spaces and study their relationships. We prove that finite…

We discuss the effect that small fluctuations of local anisotropy of pressure, and energy density, may have on the occurrence of cracking in spherical compact objects, satisfying a polytropic equation of state. Two different kind of…

We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity. The nonlocal nature of the operator and the absence of…

In this paper we investigate the extension of the charged Riemannian Penrose inequality to the case where charges are present outside the horizon. We prove a positive result when the charge densities are compactly supported, and present a…

We study the Cauchy problem of the mass critical nonlinear Schrodinger equation with derivative with the 4pi mass. One has the global well-posedness in H^1 whenever "the mass is strictly less than 4pi" or whenever "the mass is equal to 4pi…