Lower semicontinuity of quasiconvex integrals.
On increment of the tangent argument along a curve
Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points
Let be a weak solution of a quasilinear elliptic equation of the growth with a measure right hand term . We estimate at an interior point of the domain , or an irregular boundary point , in terms of a norm of , a nonlinear potential of and the Wiener integral of . This quantifies the result on necessity of the Wiener criterion.
The area formula for -mappings
Let be a mapping in the Sobolev space . Then the change of variables, or area formula holds for provided removing from counting into the multiplicity function the set where is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.
-approximation of Jacobians
The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from is approximated by functions strongly in whenever . An example is shown of a function which is in but not in .
Fine localization in potential theory [Abstract of thesis]
Positive quasi-minima
Nonisolated singularities of solutions to a quasilinear elliptic system
A note on separation of sets by approximately continuous functions
Concerning the fine topology from the band
Lusin's condition (N) and mappings of the class W1, n.
Generalized dirichlet problem in nonlinear potential theory.
Absolutely continuous functions of several variables and diffeomorphisms
In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.
Approximate differentiation: Jarník points
Relaxation of multiple integrals below the growth exponent
Degenerate elliptic equations with measure data and nonlinear potentials
Mappings of finite distortion: The zero set of the Jacobian
Remarks on delta-convex functions
On a generalization of Henstock-Kurzweil integrals
We study a scale of integrals on the real line motivated by the integral by Ball and Preiss and some recent multidimensional constructions of integral. These integrals are non-absolutely convergent and contain the Henstock-Kurzweil integral. Most of the results are of comparison nature. Further, we show that our indefinite integrals are a.e. approximately differentiable. An example of approximate discontinuity of an indefinite integral is also presented.
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
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