| Abstract: |
| The investigation of problems in shape metamorphism, surface reconstruction, and image interpolation raises fundamental questions concerning the higher-order regularity of $\infty$-potentials(a class of $\infty$-harmonic functions) and their approximation by $p$-harmonic potentials. In this talk, we establish interior $C^1$ and Sobolev regularity for $\infty$-harmonic potentials in arbitrary convex ring domains, contributing to the core theory of $\infty$-Laplace equations and $L^\infty$-variational problems. This is joint work with Prof. Yi Ru-Ya Zhang and Yuan Zhou. |
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