Search results for "Approx"

showing 2 items of 922 documents

Relaxation of a weakly discontinuous functional depending on one control function

2008

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

weakly discontinuous functionalMathematical analysisType (model theory)Optimal controlControl functionSet (abstract data type)elliptic systemoptimal controlrelaxationControl theoryModeling and SimulationQA1-939Relaxation (approximation)AnalysisMathematicsMathematicsMathematical Modelling and Analysis
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Uniform rectifiability and ε-approximability of harmonic functions in Lp

2020

Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that pointwise, L∞ and Lp type ε-approximability properties of harmonic functions are all equivalent and they characterize uniform rectifiability for codimension 1 Ahlfors–David regular sets. Our results and techniques are generalizations of recent works of T. Hytönen and A. Rosén and the first author, J. M. Martell and S. Mayboroda. peerReviewed

ε-approximabilitypotentiaaliteoriaharmonic functions.mittateoriaCarleson measuresharmoninen analyysiuniform rectifiability
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