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Displaying similar documents to “A Haar-Rado type theorem for minimizers in Sobolev spaces”

Partial regularity of minimizers of higher order integrals with (, )-growth

Sabine Schemm (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider higher order functionals of the form F [ u ] = Ω f ( D m u ) d x for u : n Ω N , where the integrand f : m ( n , N ) , m 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition γ | A | p f ( A ) L ( 1 + | A | q ) for all A m ( n , N ) , with

Partial regularity of minimizers of higher order integrals with (, )-growth

Sabine Schemm (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider higher order functionals of the form F [ u ] = Ω f ( D m u ) d x for u : n Ω N , where the integrand f : m ( n , N ) , m 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition γ | A | p f ( A ) L ( 1 + | A | q ) for all A m ( n , N ) , with

On the -stabilization of the double integrator subject to input saturation

Yacine Chitour (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system ( Σ ) x ˙ ( t ) = f ( x ( t ) , u ( t ) ) , such that there exists a feedback stabilizer that renders x ˙ = f ( x , k ( x ) ) globally asymptotically stable. Moreover, for with an output map and 1 p q , we assume that there exists a 𝒦 -function such that H ( x u ) q α ( u p ) , where is the maximal solution of ( Σ ) k x ˙ ( t ) = f ( x ( t ) , k ( x ( t ) ) + u ( t ) ) , corresponding to and to the initial condition . Then, the gain function G ( H , p , q ) of given by 14.5cm G ( H , p , q ) ( X ) = def sup u p = X H ( x u ) q , is well-defined. We call profile of for any 𝒦 -function which is of the same order of magnitude...