Abstract:This paper is concerned with the nodal set of weak solutions to a broken quasilinear partial differential equation,where a+ and a− are uniformly elliptic, Dini continuous coefficient matrices, subject to a strong correlation that a+ and a− are a multiple of some scalar function to each other. Under such a structural condition, we develop an iteration argument to achieve higher-order approximation of solutions at a singular point, which is also new for standard elliptic PDEs below Hölder regime, and as a result… Show more
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