Displaying similar documents to “A PU-integral on an abstract metric space”

The obstacle problem for functions of least gradient

William P. Ziemer, Kevin Zumbrun (1999)

Mathematica Bohemica

Similarity:

For a given domain Ω ⊂ ℝ n , we consider the variational problem of minimizing the L 1 -norm of the gradient on Ω of a function u with prescribed continuous boundary values and satisfying a continuous lower obstacle condition u ≥ ψ inside Ω . Under the assumption of strictly positive mean curvature of the boundary ∂ Ω , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle...

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

Similarity:

n this paper we investigate systems of linear integral equations in the space 𝔾 L n of n -vector valued functions which are regulated on the closed interval [ 0 , 1 ] (i.e. such that can have only discontinuities of the first kind in [ 0 , 1 ] ) and left-continuous in the corresponding open interval ( 0 , 1 ) . In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where f ∈ 𝔾 L n , the columns of the n × n -matrix valued function A belong to 𝔾 L n , the entries of B ( t , . ) have a bounded variation...

Linear Stieltjes integral equations in Banach spaces

Štefan Schwabik (1999)

Mathematica Bohemica

Similarity:

Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in []. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. []). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the...