相关论文: Interior Estimates for the $n$-dimensional Abreu's…
The aim of this paper is to discuss the theory of Newtonian and relativistic polytropes with generalized polytropic equation of state. For this purpose, we formulated the general framework to discuss the physical properties of polytrops…
Let $2\le n\le 5$. We establish an apriori interior H\"older regularity of $C^2$-stable solutions to the semilinear equation $-\Delta u=f(u)$ in any domain of $R^n$ for any nonlinearity $f\in C^{0,1}(R) $.If $f $ is nondecreasing and convex…
We propose a notion of stability for constant k-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means…
In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Amp\`ere equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates…
We extend to the anisotropic setting the existence of solutions for the Kirchhoff-Plateau problem and its dimensional reduction.
In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane--Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both the…
We prove stability estimates for the problem of recovering the nonlinearity from scattering data. We focus our attention on nonlinear Schr\"odinger equations of the form \[ (i\partial_t+\Delta)u = a(x)|u|^p u \] in three space dimensions,…
In this paper, we study the interior $C^2$ regularity problem for the Hessian quotient equation $\left(\frac{\sigma_n}{\sigma_k}\right)(D^2u)=f$. We give a complete answer to this longstanding problem: for $k=n-1,n-2$, we establish an…
We consider a steady state $v_{0}$ of the Euler equation in a fixed bounded domain in $\mathbf{R}^{n}$. Suppose the linearized Euler equation has an exponential dichotomy of unstable and center-stable subspaces. By rewriting the Euler…
In this paper, we study the polynomial stability of analytical solution and convergence of the semi-implicit Euler method for non-linear stochastic pantograph differential equations. Firstly, the sufficient conditions for solutions to grow…
We prove optimal pointwise Schauder estimates in the spatial variables for solutions of linear parabolic integro-differential equations. Optimal H\"older estimates in space-time for those spatial derivatives are also obtained.
We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms…
In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…
We consider the interior inverse problem associated with the global conservative {multipeakon} solution of the Camassa-Holm equation. Based on the inverse spectral theory on the half-line and the oscillation property of eigenfunctions, some…
In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schr\"odinger and Hartree equations on the d-dimensional torus when d=1,2,3. Due to the focusing nature of the nonlinearity in these PDEs, Gibbs…
We prove an endpoint multilinear estimate for the $X^{s,b}$ spaces associated to the periodic Airy equation. As a consequence we obtain sharp local well-posedness results for periodic generalized KdV equations, as well as some global…
We are concerned with the non-stationary Stokes system with non-homogeneous external force and non-zero initial data in ${\mathbb R}^n_+ \times (0,T)$. We obtain new estimates of solutions including pressure in terms of mixed anisotropic…
We find some bounds for the internal radii of stable and unstable manifolds of points in terms of their Lyapunov exponents under the assumption of the existence of a dominated splitting.