The partial regularity for minimizers of splitting type variational integrals under general growth conditions II. The nonautonomous case

2010 ◽  
Vol 166 (3) ◽  
pp. 259-281 ◽  
Author(s):  
D. Breit
Keyword(s):  
Partial Regularity ◽  
Growth Conditions ◽  
General Growth ◽  
Variational Integrals ◽  
Splitting Type ◽  
Nonautonomous Case

scholarly journals Higher integrability for variational integrals with non-standard growth

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Mathias Schäffner
Keyword(s):  
Partial Regularity ◽  
Growth Conditions ◽  
Integral Functionals ◽  
Restrictive Assumption ◽  
Higher Integrability ◽  
Variational Integrals

AbstractWe consider autonomous integral functionals of the form $$\begin{aligned} {\mathcal {F}}[u]:=\int _\varOmega f(D u)\,dx \quad \text{ where } u:\varOmega \rightarrow {\mathbb {R}}^N, N\ge 1, \end{aligned}$$ F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled (p, q)-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $${\mathcal {F}}$$ F assuming $$\frac{q}{p}<1+\frac{2}{n-1}$$ q p < 1 + 2 n - 1 , $$n\ge 3$$ n ≥ 3 . This improves earlier results valid under the more restrictive assumption $$\frac{q}{p}<1+\frac{2}{n}$$ q p < 1 + 2 n .

scholarly journals A new proof of semicontinuity by Young measures and an approximation theorem in Orlicz-Sobolev spaces

2003 ◽  
Vol 2003 (15) ◽  
pp. 881-898
Author(s):  
Barbara Bianconi
Keyword(s):  
Sobolev Spaces ◽  
Lower Semicontinuity ◽  
Approximation Theorem ◽  
Growth Conditions ◽  
Young Measures ◽  
New Approach ◽  
General Growth ◽  
Variational Integrals

We give a new approach to study the lower semicontinuity properties of nonautonomous variational integrals whose energy densities satisfy general growth conditions. We apply the theory of Young measures and properties of Orlicz-Sobolev spaces to prove semicontinuity result.

scholarly journals Regularity under sharp anisotropic general growth conditions

2009 ◽  
Vol 11 (1) ◽  
pp. 67-86
Author(s):  
Giovanni Cupini ◽  
◽  
Paolo Marcellini ◽  
Elvira Mascolo
Keyword(s):  
Growth Conditions ◽  
General Growth
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