Related papers: Kernel estimates for parabolic systems of partial …

We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing…

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and…

We provide quantitative gradient bounds for solutions to certain parabolic equations with unbalanced polynomial growth and non-smooth coefficients.

We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.

We consider a system of linear equations, whose coefficients depend linearly on interval parameters. Its solution set is defined as the set of all solutions of all admissible realizations of the parameters. We study unbounded directions of…

Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…

We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent…

We present some results in the analysis of non-compact differential equations on unbounded domains.

In this work, we consider a class of second order uniformly elliptic operators with smooth and bounded coefficients. We provide some estimates on the norm of the semigroup generated by these operators acting on weighted Sobolev spaces,…

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be…

One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…

Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift

In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non necessarily symmetric which could be interpreted as a non-local drift with the same order as the…

The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…

Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every…

This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems,…

We study a nonlocal parabolic equation with an irregular kernel coefficient to establish higher H\"older regularity under an appropriate higher integrablilty on the nonhomogeneous terms and a minimal regularity assumption on the kernel…

Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…

We determine sufficient conditions for the occurrence of a pointwise gradient estimate for the evolution operators associated to nonautonomous second order parabolic operators with (possibly) unbounded coefficients. Moreover we exhibit a…

This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we consider rough paths of low time regularity…