Abstract
We establish higher differentiability results for local solutions of elliptic systems of the type
in a bounded open set in ℝ2. The operator A(x, ξ) is assumed to be strictly monotone and Lipschitz continuous with respect to variable ξ. The novelty of the paper is that we allow discontinuous dependence with respect to the x-variable, through a suitable Sobolev function.
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Passarelli di Napoli, A. Higher Differentiability of Solutions of Elliptic Systems with Sobolev Coefficients: The Case p = n = 2. Potential Anal 41, 715–735 (2014). https://doi.org/10.1007/s11118-014-9390-0
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DOI: https://doi.org/10.1007/s11118-014-9390-0