This manuscript demonstrates regularity estimates of solutions to nonlinear elliptic transmission problems, indicating significant implications for mathematical modeling.
This manuscript focuses on borderline, gradient, and higher regularity estimates of solutions to fully nonlinear elliptic transmission problems given by $$ {\{ {array}{ll} {array}{lclcccl} F^+(D^2 u) & = & f^+(x) & in & Ω ^+ & = & B_1 ∩ \{ x_n > ψ (x') \}, \\ F^-(D^2 u) & = & f^-(x) & in & Ω ^- & = & B_1 ∩ \{ x_n < ψ (x') \}, \\ u^+_ν - u^-_ν & = & g(x) & on & Γ ψ & = & B_1 ∩ \{ x_n = ψ (x') \}, {array} {array}. } $$ F + ( D 2 u ) = f + ( x ) in Ω + = B 1 ∩ { x n > ψ ( x ′ ) } , F - ( D 2 u ) = f - ( x ) in Ω - = B 1 ∩ { x n < ψ
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Bessa et al. (2026) studied this question.
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