Homeomorphism with zero jacobian: Sharp integrability of the derivative

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1 Robert Èerný Homeomorphism with zero jacobian: Sharp integrability of the derivative MATH-KMA-2010/328 April 2010 Submitted Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, , Praha 8, Czech Republic

2 Cover print by Reprostredisko, Malostranske nam. 25, Praha 1 - Mala Strana Design by Mirko Rokyta, picture of snowake by Ondrej Kalenda Current series administrators: Stanislav Hencl, Ondrej Kalenda

3 List of preprints released in this series All preprints available on contact to series administrator:

4 1999 { 2008 For the details on papers submitted in specied years see the web page of the preprint series MATH-KMA-2009/292 MATH-KMA-2009/293 MATH-KMA-2009/294 MATH-KMA-2009/295 MATH-KMA-2009/296 MATH-KMA-2009/297 MATH-KMA-2009/298 MATH-KMA-2009/299 MATH-KMA-2009/300 MATH-KMA-2009/301 MATH-KMA-2009/302 MATH-KMA-2009/303 MATH-KMA-2009/304 MATH-KMA-2009/305 MATH-KMA-2009/306 MATH-KMA-2009/307 MATH-KMA-2009/308 MATH-KMA-2009/309 MATH-KMA-2009/310 MATH-KMA-2009/311 MATH-KMA-2009/312 MATH-KMA-2009/313 MATH-KMA-2009/314 MATH-KMA-2009/315 MATH-KMA-2009/316 MATH-KMA-2009/317 MATH-KMA-2009/318 MATH-KMA-2009/319 MATH-KMA-2009/320 Petr Hajek, Antonin Prochazka: C k -smooth approximations of LUR norms Martin Koc: Upper porous sets in metric which are not -lower porous Robert Cerny, Silvie Maskova: On generalization of Moserstheorem in the critical case Piotr Hajlasz, Jan Maly: On approximate dierentiability of the maximal function Robert Cerny, Silvie Maskova: A sharp form of an embedding into multiple exponential W. Desch, E. Fasangova, J. Milota, G. Propst: Spectrum of a viscoelastic boundary damping problem W. Desch, E. Fasangova, J. Milota, G. Propst: Stabilization through viscoelastic boundary damping Jan Rataj, Ludek Zajicek: Properties of distance functions on convex surfaces and Alexandrov Stanislav Hencl: Sharpness of the assumptions for the regularity of a homeomorphism Robert Cerny: Note on the lower semicontinuity with respect to the weak topology on W 1;p () Jakub Duda, Ludek Zajicek: On vector-valued curves that allow a C 1; parametrization Jiri Spurny: Weights of boundaries of compact convex sets David A. Edwards, Ondrej Kalenda, Jiri Spurny: A note on intersections of simplices Martin Koc: On relations among metric derived numbers Domingo Garcia, Ondrej Kalenda, Manuel Maestr: Envelopes of open sets and extending holomorphic functions on dual Banach Stanislav Hencl, Jan Maly: Jacobians of Sobolev homeomorphisms Petr Holicky, Roman Pol: On a question by Alexey Ostrovsky concerning preservation of completeness Lukas Maly: Calderon-type theorems for operators of non-standard endpoint behavior on Lorentz Petr Holicky: Preservation of completeness by some continuous maps Lubo Pick: Weighted inequalities for integral and supremum operators Petr Holický: Descriptive classes of sets in nonseparable Maurizio Grasselli, Dalibor Prazak, Giulio Schimperna: Attractors for nonlinear reactiondiusion systems in unbounded domains via the method of short trajectories Antonio Aviles, Ondrej Kalenda: Compactness in Banach space theory - selected problems Josef Danecek, Oldrich John, Jana Stara: Morrey space regularity for weak solutions of Stokes systems with VMO coecients Dalibor Prazak, Kumbakonam R. Rajagopal: Mechanical oscillators described by a system of dierential-algebraic equations Pavel Ludvik, Jiri Spurny : Isomorphisms of of continuous ane functions on compact convex sets with Lindelof boundaries Jiøí Spurný: Distances to of ane Baire one functions Martin Koc: Upper porosity with respect to measures Ondøej Kurka: On binormality in non-separable Banach

5 2010 MATH-KMA-2010/321 MATH-KMA-2010/322 MATH-KMA-2010/323 MATH-KMA-2010/324 MATH-KMA-2010/325 MATH-KMA-2010/326 MATH-KMA-2010/327 MATH-KMA-2010/328 Jan Rataj, Ludìk Zajíèek: Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski Stanislav Hencl: Sobolev homeomorphism with zero jacobian almost everywhere Stanislav Hencl, Jan Malý, Lubo¹ Pick, Jan Vybíral: Weak estimates cannot be obtained by extrapolation H. Bendová and J. Malý: An elementary way to introduce a Perron-like integral Ludìk Zajíèek: A note on propagation of singularities of semiconcave functions of two variables Robert Èerný, Petr Gurka, Stanislav Hencl: Concentration compactness principle for generalized Trudinger inequalities Robert Èerný: Concentration-Compactness principle for embeddings into multiple exponential Robert Èerný: Homeomorphism with zero jacobian: Sharp integrability of the derivative

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