Regularity results for a class of obstacle problems

Michela Eleuteri

Applications of Mathematics (2007)

  • Volume: 52, Issue: 2, page 137-170
  • ISSN: 0862-7940

Abstract

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We prove some optimal regularity results for minimizers of the integral functional ∫ f ( x , u , D u ) d x belonging to the class K : = { u ∈ W 1 , p ( Ω ) u ≥ ψ } , where ψ is a fixed function, under standard growth conditions of p -type, i.e. L - 1 | z | p ≤ f ( x , s , z ) ≤ L ( 1 + | z | p ) .

How to cite

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Eleuteri, Michela. "Regularity results for a class of obstacle problems." Applications of Mathematics 52.2 (2007): 137-170. <http://eudml.org/doc/33281>.

@article{Eleuteri2007,
abstract = {We prove some optimal regularity results for minimizers of the integral functional $\int f(x,u,Du)\mathrm \{d\}x$ belonging to the class $ K:=\lbrace u \in W^\{1,p\}(\Omega )\: u\ge \psi \rbrace $, where $\psi $ is a fixed function, under standard growth conditions of $p$-type, i.e. \[ L^\{-1\}|z|^p \le f(x,s,z) \le L(1+|z|^p). \]},
author = {Eleuteri, Michela},
journal = {Applications of Mathematics},
keywords = {regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions; regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions},
language = {eng},
number = {2},
pages = {137-170},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regularity results for a class of obstacle problems},
url = {http://eudml.org/doc/33281},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Eleuteri, Michela
TI - Regularity results for a class of obstacle problems
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 2
SP - 137
EP - 170
AB - We prove some optimal regularity results for minimizers of the integral functional $\int f(x,u,Du)\mathrm {d}x$ belonging to the class $ K:=\lbrace u \in W^{1,p}(\Omega )\: u\ge \psi \rbrace $, where $\psi $ is a fixed function, under standard growth conditions of $p$-type, i.e. \[ L^{-1}|z|^p \le f(x,s,z) \le L(1+|z|^p). \]
LA - eng
KW - regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions; regularity results; local minimizers; integral functionals; obstacle problems; standard growth conditions
UR - http://eudml.org/doc/33281
ER -

References

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