We study the existence and uniqueness of mild strong solutions nonlocal nonlinear diffusion problems $p$-Laplacian type with boundary conditions posed in metric random walk spaces. These spaces include, among others, weighted discrete graphs $\mathbb{R}^N$ a induced by nonsingular kernel. also case dynamical conditions. The generality nonlinearities considered allow us to cover counterparts lar...

We study the regularity of solutions to a nonlocal variational problem, which is related image denoising model, and we show that, in two dimensions, minimizers have same Hölder as original image. More precisely, if datum (locally) [Formula: see text]-Hölder continuous for some text], where text] parameter operator, prove that solution also continuous.

Abstract We prove a full Harnack inequality for local minimizers, as well weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are boundedness and functions in corresponding De Giorgi class. This paper builds upon recent work on regularity estimates such by the same authors.

Abstract A challenging task in nonlocal continuum mechanics consists formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted overcome issues inherent applicability of Eringen’s pure theory nanostructures, such as local/nonlocal mixtures elasticity and integral models involving modified averaging kernels. These can be applied the ill-pos...