| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 58 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/cocv/2024047 | |
| Published online | 28 August 2024 | |
Well-posedness for a transmission problem connecting first and second-order operators
Department of Mathematics, CIMAT, Guanajuato, Mexico
* Corresponding author: hector.chang@cimat.mx
Received:
4
July
2023
Accepted:
29
May
2024
We establish the existence and uniqueness of viscosity solutions within a domain Ω ⊆ ℝn for a class of equations governed by elliptic and eikonal type equations in disjoint regions. Our primary motivation stems from the Hamilton-Jacobi equation that arises in the context of a stochastic optimal control problem.
Mathematics Subject Classification: 35D40 / 35B51 / 35F21 / 49L12 / 49L25
Key words: Discontinuous dynamics / transmission problems / viscosity solutions / comparison principle
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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