Related papers: Gradient estimates for a class of anisotropic nonl…
Non-local equations of motion contain an infinite number of derivatives and commonly appear in a number of string theory models. We review how these equations can be rewritten in the form of a diffusion-like equation with non-linear…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously…
We present a theoretical framework on non-local classical field theory using fractional integrodifferential operators. Due to the lack of easily manageable symmetries in traditional fractional calculus and the difficulties that arise in the…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…
We propose a natural family of higher-order partial differential equations generalizing the second-order Klein-Gordon equation. We characterize the associated model by means of a generalized action for a scalar field, containing…
We study non-local exchange and scattering operators arising in domain decomposition algorithms for solving elliptic problems on domains in $\mathbb{R}^2$. Motivated by recent formulations of the Optimized Schwarz Method introduced by…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
We express a certain complex-valued solution of Legendre's differential equation as the product of an oscillatory exponential function and an integral involving only nonoscillatory elementary functions. By calculating the logarithmic…
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a…
In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…
In this brief note we discuss local H\"older continuity for solutions to anisotropic elliptic equations of the type $ \sum_{i=1}^s \partial_{ii} u+ \sum_{i=s+1}^N \partial_i \bigg(A_i(x,u,\nabla u) \bigg) =0,$ for $x \in \Omega \subset…
We propose a Nitsche method for multiscale partial differential equations, which retrieves the macroscopic information and the local microscopic information at one stroke. We prove the convergence of the method for second order elliptic…
We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the…
The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
We prove some regularity estimates for viscosity solutions to a class of possible degenerate and singular integro-differential equations whose leading operator switches between two different types of fractional elliptic phases, according to…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…