Abstract: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.
From: Fabian Fuchs [view email]
[v1]
Wed, 3 Dec 2025 17:44:56 UTC (41 KB)
[v2]
Thu, 3 Sep 2026 15:06:05 UTC (108 KB)
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