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<p>This paper studies, in the spirit of Soria-Carro and Stinga (Adv Math 435:1–51, 2023), Schauder theory to transmission problems modelled by fully nonlinear uniformly elliptic equations of second order. We focus on operators <i>F</i> that fails to be concave or convex in the space of symmetric matrices. As a consequence, in the first case it is considered that <i>F</i> enjoys a small ellipticity aperture and 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).</p>

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

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • G. C. Ricarte,
  • C. S. Barroso,
  • L. S. Tavares

摘要

This paper studies, in the spirit of Soria-Carro and Stinga (Adv Math 435:1–51, 2023), 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. As a consequence, in the first case it is considered that F enjoys a small ellipticity aperture and 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).