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Interfaces and Free Boundaries


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Volume 22, Issue 1, 2020, pp. 119–129
DOI: 10.4171/IFB/434

Published online: 2020-04-15

Well-posedness for degenerate elliptic PDE arising in optimal learning strategies

Tim Laux[1] and J. Miguel Villas-Boas[2]

(1) University of California, Berkeley, USA
(2) University of California, Berkeley, USA

We derive a comparison principle for a degenerate elliptic partial differential equation without boundary conditions which arises naturally in optimal learning strategies. Our argument is direct and exploits the degeneracy of the differential operator to construct (logarithmically) diverging barriers.

Keywords: Viscosity solutions, degenerate elliptic PDE, comparison principle

Laux Tim, Villas-Boas J. Miguel: Well-posedness for degenerate elliptic PDE arising in optimal learning strategies. Interfaces Free Bound. 22 (2020), 119-129. doi: 10.4171/IFB/434