3 citations · 6 across the 12 of their papers we have counts for
12 papers
Nonlocal Boundary Conditions for Truncated-Fractional Differential Equations Posed on Bounded Domains
Mikil Foss, Adam Larios, Michael Pieper
Nonlocal models have found great success in recent years. In particular, models that replace spatial derivatives with strongly singular integral operators involving finite interact…
A Neural Network Algorithm for KL Divergence Estimation with Quantitative Error Bounds
Mikil Foss, Andrew Lamperski
Estimating the Kullback-Leibler (KL) divergence between random variables is a fundamental problem in statistical analysis. For continuous random variables, traditional information-…
Nonlocal Ordered Mean Curvature with Integrable Kernel
Animesh Biswas, Mikil D Foss, Petronela Radu
In this paper we introduce and study the concept of nonlocal ordered curvature. In the classical (differential) setting, the problem was introduced by Nirenberg and Li, where they…
Nonlocal Differential Operators with Integrable, Nonsymmetric Kernels: Part I--Operator Theoretic Properties
Mikil Foss, Michael Pieper
Recent decades have provided a host of examples and applications motivating the study of nonlocal differential operators. We discuss a class of such operators acting on bounded dom…
Nonlocal Green theorems and Helmholtz decompositions for truncated fractional gradients
José C. Bellido, Javier Cueto, Mikil Foss +1
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite suppor…
Nonlocal Mean Curvature with Integrable Kernel
Animesh Biswas, Mikil Foss, Petronela Radu
We study the prescribed constant mean curvature problem in the nonlocal setting where the nonlocal curvature has been defined as $$ H^J_Ω(x):=\int_{\mathbb{R} ^n} J(x-y)(χ_{Ω^c}(y)…
-caloric approximation and partial regularity for parabolic systems with Orlicz growth
Mikil Foss, Teresa Isernia, Chiara Leone +1
We prove a new -caloric approximation lemma compatible with an Orlicz setting. With this result, we establish a partial regularity result for parabolic systems of the…
Sensitivity analysis for solutions to heterogeneous nonlocal systems
Nicole Buczkowski, Mikil Foss, Michael Parks +1
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators app…
Convergence Analysis and Numerical Studies for Linearly Elastic Peridynamics with Dirichlet-Type Boundary Conditions
Mikil Foss, Petronela Radu, Yue Yu
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditio…
Traces on General Sets in for Functions with no Differentiability Requirements
Mikil Foss
This paper is concerned with developing a theory of traces for functions that are integrable but need not possess any differentiability within their domain. Moreover, the domain ca…
Nonlocal Poincaré Inequalities for Integral Operators with Integrable Nonhomogeneous Kernels
Mikil Foss
The paper provides two versions of nonlocal Poincaré-type inequalities for integral operators with a convolution-type structure and functions satisfying a zero-Dirichlet like condi…
Existence and regularity of minimizers for nonlocal energy functionals
Mikil D. Foss, Petronela Radu, Cory Wright
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal…