A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917122468216832 |
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| author | Della Corte, Serena Fuchs, Fabian Kraaij, Richard C. Nendel, Max |
| author_facet | Della Corte, Serena Fuchs, Fabian Kraaij, Richard C. Nendel, Max |
| contents | This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous treatment of diffusive as well as jump terms. Estimates in the proof of the comparison principle incorporate the use of Lyapunov functions that act as growth bounds for the solutions, effectively yielding a theory for unbounded viscosity solutions. We apply the results to a wide class of parabolic equations and elliptic problems on a space with corners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04005 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary Della Corte, Serena Fuchs, Fabian Kraaij, Richard C. Nendel, Max Analysis of PDEs Probability Primary 35D40, 45K05, Secondary 35J66, 35K61, 49L25, 49Q22 This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test function framework, that allows for the simultaneous treatment of diffusive as well as jump terms. Estimates in the proof of the comparison principle incorporate the use of Lyapunov functions that act as growth bounds for the solutions, effectively yielding a theory for unbounded viscosity solutions. We apply the results to a wide class of parabolic equations and elliptic problems on a space with corners. |
| title | A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary |
| topic | Analysis of PDEs Probability Primary 35D40, 45K05, Secondary 35J66, 35K61, 49L25, 49Q22 |
| url | https://arxiv.org/abs/2512.04005 |