Work

Exterior Nonlocal Variational Inequalities

Year: 2024

Type: preprint

Abstract: This paper introduces a new class of variational inequalities where the obstacle is placed in the exterior domain that is disjoint from the observation domain. This is carried out with the help of nonlocal fractional operators. The need for such novel variational inequalities stems from the fact that the classical approach only allows placing the obstacle either inside the observation domain or on the boundary. A complete analysis of the continuous problem is provided. Additionally, perturbation arguments to approximate the problem are discussed.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.12533

Authors: Antil, Harbir, Horton, Madeline O., Warma, Mahamadi

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research, Army Research Office

Awards: Algorithms and Numerical Methods for Optimization with Partial Differential Equation Constraints, G3327059554, G6098521345, G6673636002, G7452299184, G8876996369

OpenAlex ID: W4392019905

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