Extremal Tests for Scalar Functions of Several Real variables at Degenerate Critical Points. (Short Communication).
Functions with prescribed singularities
The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the map we construct...
Further Critical Cases of the Scalar Implicit Function Theorem.
Hessian determinants as elements of dual Sobolev spaces
In this short note we present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space.
Inequalities for Jacobians: interpolation techniques
Injectivity onto a star-shaped set for local homeomorphisms in n-space
We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function...
Inverse Function Theorems and Jacobians over Metric Spaces
We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
K jedné matematické úloze o vlasech
Lebesgue measure and mappings of the Sobolev class
We present a survey of the Lusin condition (N) for -Sobolev mappings defined in a domain G of . Applications to the boundary behavior of conformal mappings are discussed.
Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen
Liouville type theorems for mappings with bounded (co)-distortion
We obtain Liouville type theorems for mappings with bounded -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded -codistorsion.
Mappings of finite distortion: Compactness.
Mappings of finite distortion: composition operator.
Mappings of finite distortion : discreteness and openness for quasi-light mappings
Mappings of finite distortion: The zero set of the Jacobian
Note zu dem Aufsatze "über eine Eigenschaft von Functionaldeterminanten" Bd. 69, p. 355 dieses Journals.
On a coregular division of a differential space by an equivalence relation
On a generalization of the Darboux theorem to the multidimensional case.
On a new class of elastic deformations not allowing for cavitation
On a set in under coordinate transformations