Related papers: Smoothing estimates for non-dispersive equations

We consider the periodic dispersion generalized Benjamin-Ono equations with polynomial nonlinearity. We establish the nonlinear smoothing properties of these equations, according to which the difference between the solution and the linear…

We consider the Cauchy problem for incompressible Navier-Stokes equations $u_t+u\nabla_xu-\Delta u+\nabla p=0, div u=0 in R^d \times R^+$ with initial data $a\in L^d(R^d)$, and study in some detail the smoothing effect of the equation. We…

Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi: \mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the…

Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…

This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…

Generalized and Simulated Method of Moments are often used to estimate structural Economic models. Yet, it is commonly reported that optimization is challenging because the corresponding objective function is non-convex. For smooth…

In this paper, we investigate interior gradient estimates for solutions to the mean curvature equation $$ \dive \left( \frac{\nabla u}{\sqrt{1 + |\nabla u|^2}} \right) = f(\nabla u)$$ under various nonlinear assumptions on the right-hand…

In this paper, we study the dispersive decay estimates for solution to the $3\mathrm{D}$ energy-critical nonlinear Schr\"odinger equation with an inverse-square operator $\mathcal{L}_a$ where the operator is denoted by…

Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address…

Let $(M,g)$ be a complete non-compact Riemannian manifold with the $m$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive…

In several cases of nonlinear dispersive PDEs, the difference between the nonlinear and linear evolutions with the same initial data, i.e. the integral term in Duhamel's formula, exhibits improved regularity. This property is usually called…

This article is concerned with one dimensional dispersive flows with cubic nonlinearities on the real line. In a very recent work, the authors have introduced a broad conjecture for such flows, asserting that in the defocusing case, small…

Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…

In the paper obtained equivalent system of Fredholm integral equations in the study of the Dirichlet problem for the generalized Manjeron equation with non-smooth coefficients in non-classical treatment (1), (4). When non-smooth conditions…

This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…

We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates. Among the applications are the…

This paper deals with Schr\"{o}dinger equations with potentials which are time-dependent non-smooth and at most quadratic growth. In the case where potentials are smooth with respect to spatial variables, fundamental solutions have explicit…

In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…

In this paper we deal with the initial value problem related to a family of dispersive inhomogeneous evolution equations Pu=f with variable coefficients belonging to the class of p-evolution equations, $p\geq 2$. We study the smoothing…

In this paper we investigate a sub-diffusion equation for simulating the anomalous diffusion phenomenon in real physical environment. Based on an equivalent transformation of the original sub-diffusion equation followed by the use of a…