A proof of Hessian Sobolev inequality |
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| Authors: | Shuxuan Li |
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| Institution: | Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Sciences (CAS), Wuhan 430071, PR China |
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| Abstract: | In this paper, taking the Hessian Sobolev inequality (0<p≤k) (X.-J. Wang, 1994 2]) as the starting point, we give a proof of the Hessian Sobolev inequality when k<p≤k∗, where k∗ is the critical Sobolev embedding index of k-Hessian type. We also prove that k∗ is optimal by one-dimensional Hardy’s inequality. |
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| Keywords: | Hessian Sobolev inequality Hessian equation A priori estimates |
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