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arXiv · 2304.00778

Local behaviour of the mixed local and nonlocal problems with nonstandard growth

Mengyao Ding·Yuzhou Fang·Chao Zhang
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Abstract

We consider the mixed local and nonlocal functionals with nonstandard growth \begin{eqnarray*} u\mapsto\int_{\Omega}(|Du|^p-f(x)u)\,dx+\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}\frac{|u(x)-u(y)|^q}{|x-y|^{N+sq}}\,dxdy \end{eqnarray*} with $1 sq$ in [De Filippis-Mingione, Math. Ann., https://doi.org/10.1007/s00208-022-02512-7].

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Mengyao Ding, Yuzhou Fang, Chao Zhang. 2023-04-03. Local behaviour of the mixed local and nonlocal problems with nonstandard growth. https://arxiv.org/abs/2304.00778

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