# Jacobians of Sobolev homeomorphisms

## Related Articles

- Regularity of the Inverse of a Planar Sobolev Homeomorphism. Hencl, Stanislav; Koskela, Pekka // Archive for Rational Mechanics & Analysis;Apr2006, Vol. 180 Issue 1, p75
Let [InlineMediaObject not available: see fulltext.] be a domain. Suppose that f ? W 1,1loc(O, R 2) is a homeomorphism such that Df( x) vanishes almost everywhere in the zero set of J f . We show that f -1 ? W 1,1loc( f(O), R 2) and that Df -1( y) vanishes almost everywhere in the zero set of...

- Homeomorphisms of Bounded Variation. Hencl, Stanislav; Koskela, Pekka; Onninen, Jani // Archive for Rational Mechanics & Analysis;Dec2007, Vol. 186 Issue 3, p351
We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that f -1 is of bounded variation provided that f ? W 1,1(O; R n ) is a homeomorphism with | Df| in the Lorentz space L n-1,1(O).

- ANISOTROPIC SOBOLEV HOMEOMORPHISMS. Gironimo, Patrizia Di; D'Onofrio, Luigi; Sbordone, Carlo; Schiattarella, Roberta // Annales Academiae Scientiarum Fennicae. Mathematica;2011, Vol. 36 Issue 2, p593
Let Î© â„‘ R2 be a domain. Suppose that fâˆˆ W1,1loc (Î©;R2) is a homeomorphism. Then the components x(w)1 y(w) of the inverse f-1 = (x,y) : Î©';â†’Î© have total variations given [Multiple line equation(s) cannot be represented in ASCII text].

- Exact constants in the inequalities for intermediate derivatives in n-dimensional space. Lunev, A. // Mathematical Notes;Apr2009, Vol. 85 Issue 3/4, p458
The article presents a calculation for intermediate derivatives inequalities. It recalls and defines the composition of square-integrable functions with an L2 (Rn) and the equivalent norms' class in Hm (Rn) Sobolev space by equality, respectively. Proofs of calculation based on theorems are also...

- Fractional Sobolev, Moserï¿½Trudinger, Morreyï¿½Sobolev inequalities under Lorentz norms. Xiao, J.; Zhai, Zh. // Journal of Mathematical Sciences;Apr2010, Vol. 166 Issue 3, p357
We consider the Sobolev type inequalities under Lorentz norms on bounded open domains for fractional derivatives (-?) s/2 in the following three cases: n > ps, n = ps, and n < ps, whence establishing the weak type Sobolev inequalities, Moserï¿½Trudinger and Morreyï¿½Sobolev inequalities...

- On Multiquasielliptic Equations in $R\_n$. Shmyrëv, G. A. // Siberian Mathematical Journal;Sep/Oct2003, Vol. 44 Issue 5, p926
We prove solvability of multiquasielliptic equations with constant coefficients in the Sobolev-type spaces whose norms are determined by some finite set of derivatives.

- Eigenvalue problems with weights in Lorentz spaces. Anoop, T. C.; Lucia, Marcello; Ramaswamy, Mythily // Calculus of Variations & Partial Differential Equations;Nov2009, Vol. 36 Issue 3, p355
Given V, w locally integrable functions on a general domain Î© with V â‰¥ 0 but w allowed to change sign, we study the existence of ground states for the nonlinear eigenvalue problem: with p subcritical. These are minimizers of the associated Rayleigh quotient whose existence is ensured...

- Ground State for the SchrÃ¶dinger Operator with the Weighted Hardy Potential. Chabrowski, J.; Tintarev, K. // International Journal of Differential Equations;2011, p1
We establish the existence of ground states on RN for the Laplace operator involving the Hardytype potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the...

- Conformal Weights and Sobolev Embeddings. Gol'dshtein, V.; Ukhlov, A. // Journal of Mathematical Sciences;Aug2013, Vol. 193 Issue 2, p202
We study embeddings of the Sobolev space $$ {\mathop{W}\limits_{~}^{\circ}}{{~}_2^1}\left( \Omega \right) $$ into weighted Lebesgue spaces L(Î©, h) with the so-called universal conformal weight h defined as the Jacobian of a conformal homeomorphism Ï† from Î© onto the unit disk in the...