Partial Regularity of Cartesian Currents which Minimize Certain Variational Integrals

1989 ◽  
pp. 563-587 ◽  
Author(s):  
Mariano Giaquinta ◽  
Giuseppe Modica ◽  
Jiři Souček
Keyword(s):  
Partial Regularity ◽  
Cartesian Currents ◽  
Variational Integrals

scholarly journals Partial regularity for minima of variational integrals

1987 ◽  
Vol 25 (1-2) ◽  
pp. 221-229 ◽  
Author(s):  
Mariano Giaquinta ◽  
Per-Anders Ivert
Keyword(s):  
Partial Regularity ◽  
Variational Integrals

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 .

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