Abstract
We prove existence of \({u\in C^{k}(\overline{\Omega};\mathbb{R}^{n})}\) satisfying
where k ≥ 1 is an integer, \({\Omega}\) is a bounded smooth domain and \({f\in C^{k}(\overline{\Omega}) }\) satisfies
with no sign hypothesis on f.
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Cupini, G., Dacorogna, B. & Kneuss, O. On the equation \({{\rm det}\,\nabla{u}=f}\) with no sign hypothesis. Calc. Var. 36, 251–283 (2009). https://doi.org/10.1007/s00526-009-0228-3
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DOI: https://doi.org/10.1007/s00526-009-0228-3