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Title: | Higher differentiability results for solutions to a class of non-homogeneous elliptic problems under sub-quadratic growth conditions |
Author: | Clop, Albert Gentile, Andrea Passarelli di Napoli, Antonia |
Keywords: | Funcions convexes Equacions diferencials el·líptiques Teoria de control Convex functions Elliptic differential equations Control theory |
Issue Date: | 29-May-2023 |
Publisher: | World Scientific Publishing |
Abstract: | We prove a sharp higher differentiability result for local minimizers of functionals of the form $$ \mathscr{F}(w, \Omega)=\int_{\Omega}[F(x, D w(x))-f(x) \cdot w(x)] d x $$ with non-autonomous integrand $F(x, \xi)$ which is convex with respect to the gradient variable, under $p$-growth conditions, with $1<p<2$. The main novelty here is that the results are obtained assuming that the partial map $x \mapsto D_{\xi} F(x, \xi)$ has weak derivatives in some Lebesgue space $L^q$ and the datum $f$ is assumed to belong to a suitable Lebesgue space $L^r$. We also prove that it is possible to weaken the assumption on the datum $f$ and on the map $x \mapsto D_{\xi} F(x, \xi)$, if the minimizers are assumed to be a priori bounded. |
Note: | Reproducció del document publicat a: https://doi.org/https://doi.org/10.1142/S166436072350008X |
It is part of: | Bulletin Of Mathematical Sciences, 2023, vol. 13, num.2 |
URI: | https://hdl.handle.net/2445/221444 |
Related resource: | https://doi.org/https://doi.org/10.1142/S166436072350008X |
ISSN: | 1664-3607 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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