Higher order variational inequalities with non-standard growth conditions in dimension two: plates with obstacles.
Michael Bildhauer, Martin Fuchs · Annales Academiae Scientiarum Fennicae Mathematica · 2001
For a domain › ‰ R 2 we consider the second order variational problem of minimizing J(w) = R › f(r 2 w)dx among functions w : ›! R with zero trace respecting a side condition of the form w ‚ on › . Here f is a smooth convex integrand with non-standard growth, a typical example is given by f(r 2 w) = jr 2 wj ln(1 +jr 2 wj) . We prove that|under suitable assumptions on |the unique minimizer is of class C 1;fi (›) for any fi < 1 . Our results provide a kind of interpolation between elastic and plastic plates with obstacles.