Exterior Nonlocal Variational Inequalities
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909111994548224 |
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| author | Antil, Harbir Horton, Madeline O. Warma, Mahamadi |
| author_facet | Antil, Harbir Horton, Madeline O. Warma, Mahamadi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exterior Nonlocal Variational Inequalities Antil, Harbir Horton, Madeline O. Warma, Mahamadi Analysis of PDEs Numerical Analysis Optimization and Control 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. |
| title | Exterior Nonlocal Variational Inequalities |
| topic | Analysis of PDEs Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2402.12533 |