Parabolic and elliptic systems in divergence form with variably partially BMO coefficients - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We establish the solvability of second order divergence type parabolicsystems in Sobolev spaces. The leading coefficients are assumed to be onlymeasurable in one spatial direction on each small parabolic cylinder with thespatial direction allowed to depend on the cylinder. In the other orthogonaldirections and the time variable the coefficients have locally small meanoscillations. We also obtain the corresponding $W^1 p$-solvability of secondorder elliptic systems in divergence form. Our results are new even for scalarequations and the proofs simplify the methods used previously in 12



Author: Hongjie Dong, Doyoon Kim

Source: https://arxiv.org/







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