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

DOI10.1112/JLMS.12947arXiv2304.00778MaRDI QIDQ6431805

Author name not available (Why is that?)

Publication date: 3 April 2023

Abstract: We consider the mixed local and nonlocal functionals with nonstandard growth �egin{eqnarray*} umapstoint_{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 < p l e s q

,

0 < s < 1

and

O m e g a s u b s e t m a t h b b R^{N}

being a bounded domain. We study, by means of expansion of positivity, local behaviour of the minimizers of such problems, involving local boundedness, local H"{o}lder continuity and Harnack inequality. The results above can be seen as a natural extension of the results under the center condition that

p > s q

in [De Filippis-Mingione, Math. Ann., https://doi.org/10.1007/s00208-022-02512-7].

Mathematics Subject Classification ID

No records found.

This page was built for publication: Local behaviour of the mixed local and nonlocal problems with nonstandard growth

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6431805)