Related papers: Regularity in diffusion models with gradient activ…

We consider a class of variable-exponent mixed fully nonlinear local and nonlocal degenerate elliptic equations, which degenerate along the set of critical points, $C:=\big\{x:\,Du(x)=0\big\}.$ Under general conditions, first, we establish…

We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this…

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

In this article we are interested in studying regularity up to the boundary for one-phase singularly perturbed fully nonlinear elliptic problems, associated to high energy activation potentials, namely $$ F(X, \nabla u^{\varepsilon}, D^2…

In this manuscript, we study geometric regularity estimates for degenerate parabolic equations of $p$-Laplacian type ($2 \leq p< \infty$) under a strong absorption condition: $ \Delta_p u - \frac{\partial u}{\partial t} = \lambda_0 u_{+}^q…

An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive,…

We derive a priori estimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using…

This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet,…

A class of linear degenerate elliptic equations inspired by nonlinear diffusions of image processing is considered. It is characterized by an interior degeneration of the diffusion coefficient. It is shown that no particularly natural,…

In this paper, we investigate a class of doubly nonlinear evolutions PDEs. We establish sharp regularity for the solutions in H\"older spaces. The proof is based on the geometric tangential method and intrinsic scaling technique. Our…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

We investigate the regularity of solutions to linear elliptic equations in both divergence and non-divergence forms, particularly when the principal coefficients have Dini mean oscillation. We show that if a solution $u$ to a…

We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \quad\quad\text{in}\quad\quad…

We obtain uniform in time $L^\infty$-bounds for the solutions to a class of thermo-diffusive systems. The nonlinearity is assumed to be at most sub-exponentially growing at infinity and have a linear behavior near zero.

In this paper we prove Holder regularity of the derivative of radial solutions to fully nonlinear equations when the operator is hessian, homogenous of degree 1 in the Hessian, homogenous of some degree $\alpha>-1$ in the gradient and which…

We prove sharp boundary H{\"o}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini}}$-property. This result is new even for the fractional…

It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…

In this paper we establish optimal $C^{1,\alpha}$ regularity up to the boundary for viscosity solutions of fully nonlinear elliptic equations with double phase degeneracy law and oblique boundary conditions. The approach developed here…

We study the generalization performance of unregularized gradient methods for separable linear classification. While previous work mostly deal with the binary case, we focus on the multiclass setting with $k$ classes and establish novel…

We study a continuous-time dynamical system which arises as the limit of a broad class of nonlinearly preconditioned gradient methods. Under mild assumptions, we establish existence of global solutions and derive Lyapunov-based convergence…