Differentiability for minimizers of anisotropic integrals

Paola Cavaliere; Anna D'Ottavio; Francesco Leonetti; Maria Longobardi

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 685-696
  • ISSN: 0010-2628

Abstract

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We consider a function u : Ω → ℝ N , Ω ⊂ ℝ n , minimizing the integral ∫ Ω ( | D 1 u | 2 + ⋯ + | D n - 1 u | 2 + | D n u | p ) d x , 2 ( n + 1 ) / ( n + 3 ) ≤ p < 2 , where D i u = ∂ u / ∂ x i , or some more general functional with the same behaviour; we prove the existence of second weak derivatives D ( D 1 u ) , ⋯ , D ( D n - 1 u ) ∈ L 2 and D ( D n u ) ∈ L p .

How to cite

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Cavaliere, Paola, et al. "Differentiability for minimizers of anisotropic integrals." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 685-696. <http://eudml.org/doc/248270>.

@article{Cavaliere1998,
abstract = {We consider a function $u:\Omega \rightarrow \mathbb \{R\}^N$, $\Omega \subset \mathbb \{R\}^n$, minimizing the integral $\int _\Omega (|D_1 u|^2 + \dots +|D_\{n-1\}u|^2 +|D_n u|^p)\,dx$, $2(n+1)/(n+3)\le p<2$, where $D_i u = \partial u/ \partial x_i$, or some more general functional with the same behaviour; we prove the existence of second weak derivatives $D(D_1 u), \dots , D(D_\{n-1\} u) \in L^2$ and $D(D_n u) \in L^p$.},
author = {Cavaliere, Paola, D'Ottavio, Anna, Leonetti, Francesco, Longobardi, Maria},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regularity; minimizers; integral functionals; anisotropic growth; regularity; minimizers; integral functionals; anisotropic growth},
language = {eng},
number = {4},
pages = {685-696},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Differentiability for minimizers of anisotropic integrals},
url = {http://eudml.org/doc/248270},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Cavaliere, Paola
AU - D'Ottavio, Anna
AU - Leonetti, Francesco
AU - Longobardi, Maria
TI - Differentiability for minimizers of anisotropic integrals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 685
EP - 696
AB - We consider a function $u:\Omega \rightarrow \mathbb {R}^N$, $\Omega \subset \mathbb {R}^n$, minimizing the integral $\int _\Omega (|D_1 u|^2 + \dots +|D_{n-1}u|^2 +|D_n u|^p)\,dx$, $2(n+1)/(n+3)\le p<2$, where $D_i u = \partial u/ \partial x_i$, or some more general functional with the same behaviour; we prove the existence of second weak derivatives $D(D_1 u), \dots , D(D_{n-1} u) \in L^2$ and $D(D_n u) \in L^p$.
LA - eng
KW - regularity; minimizers; integral functionals; anisotropic growth; regularity; minimizers; integral functionals; anisotropic growth
UR - http://eudml.org/doc/248270
ER -

References

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