Hölder continuity results for a class of functionals with non-standard growth

Michela Eleuteri

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 1, page 129-157
  • ISSN: 0392-4041

Abstract

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We prove regularity results for real valued minimizers of the integral functional ∫ f ⁢ x , u , D ⁢ u under non-standard growth conditions of p ⁢ x -type, i.e. L - 1 ⁢ z p ⁢ x ≤ f ⁢ x , s , z ≤ L ⁢ 1 + z p ⁢ x under sharp assumptions on the continuous function p ⁢ x > 1 .

How to cite

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Eleuteri, Michela. "Hölder continuity results for a class of functionals with non-standard growth." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 129-157. <http://eudml.org/doc/196144>.

@article{Eleuteri2004,
abstract = {We prove regularity results for real valued minimizers of the integral functional $\int f (x, u, Du)$ under non-standard growth conditions of $p(x)$-type, i.e. $$L^\{-1\} |z|^\{p(x)\} \leq f (x, s , z)\leq L(1+|z|^\{p(x)\})$$ under sharp assumptions on the continuous function $p(x)>1$.},
author = {Eleuteri, Michela},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {129-157},
publisher = {Unione Matematica Italiana},
title = {Hölder continuity results for a class of functionals with non-standard growth},
url = {http://eudml.org/doc/196144},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Eleuteri, Michela
TI - Hölder continuity results for a class of functionals with non-standard growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 129
EP - 157
AB - We prove regularity results for real valued minimizers of the integral functional $\int f (x, u, Du)$ under non-standard growth conditions of $p(x)$-type, i.e. $$L^{-1} |z|^{p(x)} \leq f (x, s , z)\leq L(1+|z|^{p(x)})$$ under sharp assumptions on the continuous function $p(x)>1$.
LA - eng
UR - http://eudml.org/doc/196144
ER -

References

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Citations in EuDML Documents

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  1. Sungchol Kim, Dukman Ri, C 1 , α regularity for elliptic equations with the general nonstandard growth conditions
  2. Jens Habermann, Full Regularity for Convex Integral Functionals with p ⁢ ( x ) Growth in Low Dimensions
  3. Michela Eleuteri, Regularity results for a class of obstacle problems
  4. Petteri Harjulehto, Variable exponent Sobolev spaces with zero boundary values
  5. Giuseppe Mingione, Regularity of minima: an invitation to the Dark Side of the Calculus of Variations

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