Genericity and existence of a minimum for scalar integral functionals

1995 ◽  
Vol 86 (2) ◽  
pp. 421-431 ◽  
Author(s):  
M. D. P. Monteiro Marques ◽  
A. Ornelas
Keyword(s):  
Integral Functionals ◽  
Scalar Integral

scholarly journals Growth conditions and regularity, an optimal local boundedness result

2020 ◽  
pp. 2050029
Author(s):  
Jonas Hirsch ◽  
Mathias Schäffner
Keyword(s):  
Growth Conditions ◽  
Integral Functionals ◽  
Local Minimizers ◽  
Local Boundedness ◽  
Scalar Integral ◽  
Boundedness Result

We prove local boundedness of local minimizers of scalar integral functionals [Formula: see text], [Formula: see text] where the integrand satisfies [Formula: see text]-growth of the form [Formula: see text] under the optimal relation [Formula: see text].

scholarly journals $L^{\Phi }-L^{\infty }$\ Inequalities and Applications

2015 ◽  
Vol 7 (2) ◽  
pp. 201 ◽  
Author(s):  
Tiziano Granucci
Keyword(s):  
Sobolev Space ◽  
Continuous Functions ◽  
Integral Functionals ◽  
Scalar Integral

In this paper we prove some $L^{\Phi }-L^{\Phi }$ and $L^{\Phi }-L^{\infty }$inequalities for quasi-minima of scalar integral functionals defined inOrlicz-Sobolev space $W^{1}L^{\Phi }\left( \Omega \right) $, where $\Phi $\is a N-function and $\Phi \in \triangle _{2}$. Moreover, if $\Phi \in\triangle ^{^{\prime }}$ or if $\Phi \in \triangle _{2}\cap \nabla _{2}$, weprove that quasi-minima are H\"{o}lder continuous functions.

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