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arXiv · 2404.16602

High-Order regularity for fully nonlinear elliptic transmission problems under weak convexity assumption

G. C. Ricarte·C. S. Barroso·L. S. Tavares
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Abstract

This paper studies Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators F that fails to be concave or convex in the space of symmetric matrices. In a first scenario, it is considered that F enjoys a small ellipticity aperture. In our second case, we study regularity results where the convexity of the superlevel (or sublevel) sets is verified, implying that the operator F is quasiconcave (or quasiconvex).

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G. C. Ricarte, C. S. Barroso, L. S. Tavares. 2024-04-25. High-Order regularity for fully nonlinear elliptic transmission problems under weak convexity assumption. https://arxiv.org/abs/2404.16602

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