Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some quantitative results on Lipschitz inverse and implicit functions
  theorems   Let $ f: \mathbb{R} ^ n \rightarrow \mathbb{R}^n $ be a Lipschitz mapping
with generalized Jacobian at $x_0$, denoted by $\partial f(x_0)$, is of maximal
rank. F. H. Clarke (1976) proved that $f$ is locally invertible. In this paper,
we give some quantitative assessments for Clarke's theorem on the Lipschitz
inverse, and prove that the class of such mappings are open. Moreover, we also
present a quantitative form for Lipschitz implicit function theorem.

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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess