Regularity for minimizers of non-autonomous non-quadratic functionals in the case 1<p<2: an a priori estimate

Andrea Gentile

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (2018)

  • Volume: 85, Issue: 1, page 185-200
  • ISSN: 0370-3568

Abstract

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We establish an a priori estimate for the second derivatives of local minimizers of integral functionals of the form \mathcal{F}(\nu,\Omega)=\int_{\Omega}f(x,D\nu(x))\,dx with convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.

How to cite

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Gentile, Andrea. "Regularity for minimizers of non-autonomous non-quadratic functionals in the case $1 < p < 2$: an a priori estimate." Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche 85.1 (2018): 185-200. <http://eudml.org/doc/296735>.

@article{Gentile2018,
abstract = {We establish an a priori estimate for the second derivatives of local minimizers of integral functionals of the form \begin\{equation*\}\mathcal\{F\}(\nu, \Omega) = \int\_\{\Omega\} f(x, D\nu(x))\, dx \end\{equation*\} with convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the $x$ variable belongs to a suitable Sobolev space. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.},
author = {Gentile, Andrea},
journal = {Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche},
keywords = {Local minimizers; A priori estimate; Sobolev coefficients},
language = {eng},
month = {12},
number = {1},
pages = {185-200},
publisher = {Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini},
title = {Regularity for minimizers of non-autonomous non-quadratic functionals in the case $1 < p < 2$: an a priori estimate},
url = {http://eudml.org/doc/296735},
volume = {85},
year = {2018},
}

TY - JOUR
AU - Gentile, Andrea
TI - Regularity for minimizers of non-autonomous non-quadratic functionals in the case $1 < p < 2$: an a priori estimate
JO - Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche
DA - 2018/12//
PB - Società Nazione di Scienze, Lettere e Arti in Napoli; Giannini
VL - 85
IS - 1
SP - 185
EP - 200
AB - We establish an a priori estimate for the second derivatives of local minimizers of integral functionals of the form \begin{equation*}\mathcal{F}(\nu, \Omega) = \int_{\Omega} f(x, D\nu(x))\, dx \end{equation*} with convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the $x$ variable belongs to a suitable Sobolev space. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.
LA - eng
KW - Local minimizers; A priori estimate; Sobolev coefficients
UR - http://eudml.org/doc/296735
ER -

References

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