Regularity of minimizers of W1, p -quasiconvex variational integrals with (p,q)-growth

Schmidt, Thomas
May 2008
Calculus of Variations & Partial Differential Equations;May2008, Vol. 32 Issue 1, p1
Academic Journal
We consider autonomous integrals in the multidimensional calculus of variations, where the integrand f is a strictly W 1, p -quasiconvex C 2-function satisfying the ( p, q)-growth conditions with exponents 1 < p = q < 8. Under these assumptions we establish an existence result for minimizers of F in $$W^{1,p}(\Omega;{\mathbb{R}}^N)$$ provided $$q\quad < \quad\frac{np}{n-1}$$ . We prove a corresponding partial C 1, a -regularity theorem for $$q < p +\frac{{\rm min}\{2,p\}}{2n}$$ . This is the first regularity result for autonomous quasiconvex integrals with ( p, q)-growth.


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