Related papers: Sharp decay estimates for critical Dirac equations

We study a notion of finite energy solutions to elliptic systems with power nonlinearities in R^n. We establish sharp pointwise decay estimates for positive and sign-changing solutions. By using these estimates, we obtain symmetry results…

In this paper we show the existence of infinitely many symmetric solutions for a cubic Dirac equation in two dimensions, which appears as effective model in systems related to honeycomb structures. Such equation is critical for the Sobolev…

We prove a classification result for ground state solutions of the critical Dirac equation on $\mathbb{R}^n$, $n\geq2$. By exploiting its conformal covariance, the equation can be posed on the round sphere $\mathbb{S}^n$ and the non-zero…

We prove sharp pointwise blow-up estimates for finite-energy sign-changing solutions of critical equations of Schr\"odinger-Yamabe type on a closed Riemannian manifold $(M,g)$ of dimension $n \ge 3$. This is a generalisation of the…

The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…

We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence…

We determine the largest non-trivial rate of exponential decay at infinity for solutions to the Dirac equation \begin{equation*} \mathcal{D}_n \psi + \mathbb{V} \psi = 0 \quad \text{ in }\mathbb{R}^n, \end{equation*} being $\mathcal{D}_n$…

This paper is devoted to the study of degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type. By means of blow-up analysis techniques, we prove an a-priori estimate in a weighted space of continuous functions. From this…

A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such equations, and our H\"older regularity refines certain…

We establish the decay and Strichartz estimates for the wave equation with large scaling-critical electromagnetic potentials on a conical singular space $(X,g)$ with dimension $n\geq3$, where the metric $g=dr^2+r^2 h$ and…

We study the critical dissipative quasi-geostrophic equations in $\bR^2$ with arbitrary $H^1$ initial data. After showing certain decay estimate, a global well-posedness result is proved by adapting the method in [11] with a suitable…

We prove new improved endpoint, $L^{p_c}$, $p_c=\tfrac{2(n+1)}{n-1}$, estimates (the "kink point") for eigenfunctions on manifolds of nonpositive curvature. We do this by using energy and dispersive estimates for the wave equation as well…

We investigate fourth order Paneitz equations of critical growth in the case of $n$-dimensional closed conformally flat manifolds, $n \ge 5$. Such equations arise from conformal geometry and are modelized on the Einstein case of the…

This article investigates the effect for random pinning models of long range power-law decaying correlations in the environment. For a particular type of environment based on a renewal construction, we are able to sharply describe the phase…

In this paper, we prove sharp gradient estimates for positive solutions to the weighted heat equation on smooth metric measure spaces with compact boundary. As an application, we prove Liouville theorems for ancient solutions satisfying the…

We study the critical and super-critical dissipative quasi-geostrophic equations in $\bR^2$ or $\bT^2$. Higher regularity of mild solutions with arbitrary initial data in $H^{2-\gamma}$ is proved. As a corollary, we obtain a global…

The open question, which seems to be also the final part, in terms of studying the Cauchy problem for the weakly coupled system of damped wave equations or reaction-diffusion equations, is so far known as the sharp lifespan estimates in the…

The strong decays of $D_1(2420)^0$, $D_2^*(2460)^0$, $D_2^*(2460)^+$, $D_2^*(2460)^-$, $D(2550)^0$, $D_J^*(2600)^0$, $D(2740)^0$, $D_3^*(2750)^0$, $D_3^*(2750)^+$, $D_3^*(2750)^-$, $D_J(3000)^0$, $D{_{J}^*}(3000)^0$ and $D_2^*(3000)^0$…

In this paper we provide the classification of positive solutions to the critical $p-$Laplace equation on $\mathbb{R}^n$, for $1<p<n$, possibly having infinite energy. If $n=2$, or if $n=3$ and $\frac 32<p<2$ we prove rigidity without any…

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold $M^n$ admitting real Killing spinors (resp. parallel spinors), there…