Integrability for vector-valued minimizers of some variational integrals

Francesco Leonetti; Francesco Siepe

Commentationes Mathematicae Universitatis Carolinae (2001)

  • Volume: 42, Issue: 3, page 469-479
  • ISSN: 0010-2628

Abstract

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We prove that the higher integrability of the data f , f 0 improves on the integrability of minimizers u of functionals ℱ , whose model is ∫ Ω | D u | p + ( det ( D u ) ) 2 - 〈 f , D u 〉 + 〈 f 0 , u 〉 d x , where u : Ω ⊂ ℝ n → ℝ n and p ≥ 2 .

How to cite

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Leonetti, Francesco, and Siepe, Francesco. "Integrability for vector-valued minimizers of some variational integrals." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 469-479. <http://eudml.org/doc/248821>.

@article{Leonetti2001,
abstract = {We prove that the higher integrability of the data $f, f_0$ improves on the integrability of minimizers $u$ of functionals $\mathcal \{F\}$, whose model is \[ \int \_\{\Omega \} \left[|Du|^p + (\operatorname\{det\} (Du))^2 - \langle f,Du \rangle + \langle f\_0,u \rangle \right] dx, \] where $u:\Omega \subset \mathbb \{R\}^n\rightarrow \mathbb \{R\}^n$ and $p\ge 2$.},
author = {Leonetti, Francesco, Siepe, Francesco},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {calculus of variations; minimizers; regularity; multidimensional vectorial variational problem; minimizers; regularity },
language = {eng},
number = {3},
pages = {469-479},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Integrability for vector-valued minimizers of some variational integrals},
url = {http://eudml.org/doc/248821},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Leonetti, Francesco
AU - Siepe, Francesco
TI - Integrability for vector-valued minimizers of some variational integrals
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 469
EP - 479
AB - We prove that the higher integrability of the data $f, f_0$ improves on the integrability of minimizers $u$ of functionals $\mathcal {F}$, whose model is \[ \int _{\Omega } \left[|Du|^p + (\operatorname{det} (Du))^2 - \langle f,Du \rangle + \langle f_0,u \rangle \right] dx, \] where $u:\Omega \subset \mathbb {R}^n\rightarrow \mathbb {R}^n$ and $p\ge 2$.
LA - eng
KW - calculus of variations; minimizers; regularity; multidimensional vectorial variational problem; minimizers; regularity
UR - http://eudml.org/doc/248821
ER -

References

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  9. Giusti E., Metodi diretti nel calcolo delle variazioni, U.M.I., 1994. Zbl0942.49002MR1707291
  10. Kufner A., John O., Fučik S., Function Spaces, Noordhoff International Publishing, Leyden, 1977. MR0482102
  11. Leonetti F., Maximum principle for vector-valued minimizers of some integral functionals, Boll. Un. Mat. Ital. 7 (1991), 51-56. (1991) Zbl0729.49015MR1101010
  12. Leonetti F., Maximum principle for functionals depending on minors of the jacobian matrix of vector-valued mappings, Australian Nat. Univ., Centre for Math. Anal., Research Report 20, 1990. 
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