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An Aronsson type approach to extremal quasiconformal mappings
 J. Differential Equations, Volume 253, Issue
, 2012
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Monotonicity formulas for variational problems
"... 1.1 Monotonicity and entropy methods. This expository paper is a revision of a short talk I gave at a meeting on convexity and entropy methods at The Kavli Royal Society International Centre at Chicheley Hall during June, 2011. Most of the lectures concerned “entropy ” methods for partial differenti ..."
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1.1 Monotonicity and entropy methods. This expository paper is a revision of a short talk I gave at a meeting on convexity and entropy methods at The Kavli Royal Society International Centre at Chicheley Hall during June, 2011. Most of the lectures concerned “entropy ” methods for partial differential equations, which mostly mean discovering and
New Convexity Conditions in the Calculus of Variations and Compensated Compactness
, 2003
"... We consider the lower semicontinuous functional of the form I f (u) = f(u)dx where u satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar's { convexity condition ..."
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We consider the lower semicontinuous functional of the form I f (u) = f(u)dx where u satisfies a given conservation law defined by differential operator of degree one with constant coefficients. We show that under certain constraints the well known Murat and Tartar's { convexity condition for the integrand f extends to the new geometric conditions satisfied on four dimensional simplexes. Similar conditions on three dimensional simplexes were recently obtained by the second author. New conditions apply to quasiconvex functions.
Lusin type theorem with quasiconvex hulls
"... We obtain Lusin type theorem showing that after extracting an open set of an arbitrary small measure one can apply some variant of convex integration theory using quasiconvex hulls of sets instead of lamconvex hulls (called by Gromov Pconvex hulls in the more general setting) or rankone convex hu ..."
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We obtain Lusin type theorem showing that after extracting an open set of an arbitrary small measure one can apply some variant of convex integration theory using quasiconvex hulls of sets instead of lamconvex hulls (called by Gromov Pconvex hulls in the more general setting) or rankone convex hulls in the approach by Müller and Sverák.