Abstract
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating our problem to a homogeneous, fully nonlinear, uniformly elliptic equation.
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Acknowledgements
The author is very grateful to E. A. Pimentel and J. M. Urbano for pointing out this problem and for the fruitful discussions they had together. DJ was supported by FCT, Portugal, through scholarship PD/BD/150354/2019, under POCH funds, co-financed by the European Social Fund and Portuguese National Funds from MEC, Portugal.
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Jesus, D. A degenerate fully nonlinear free transmission problem with variable exponents. Calc. Var. 61, 29 (2022). https://doi.org/10.1007/s00526-021-02144-w
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DOI: https://doi.org/10.1007/s00526-021-02144-w