By Elisa Davoli and others

In the context of Sobolev spaces with variable exponents, Poincar\'e--Wirtinger inequalities are possible as soon as Luxemburg norms are considered. On the other hand, modular versions of the inequalities in the expected form \begin{equation*} \int_\Omega \left|f(x)-\langle f\rangle_{\Omega}\right|^{p(x)} \ {\mathrm{d} x} \leqslant C \int_\Omega|\nabla f(x)|^{p(x)}{\mathrm{d} x}, \end{equation*} are known to be... Show more

January 30, 2024

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A modular Poincaré-Wirtinger type inequality on Lipschitz domains for Sobolev spaces with variable exponents

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