Search results for "28A25"

showing 2 items of 2 documents

A Riemann-Type Integral on a Measure Space

2005

In a compact Hausdorff measure space we define an integral by partitions of the unity and prove that it is nonabsolutely convergent.

Lebesgue measureMathematical analysisMeasure (physics)Mathematics::General Topologypartition of unityRiemann integralRiemann–Stieltjes integralLebesgue integration$PU^*$-integralsymbols.namesakeTransverse measureDifferentiation of integralssymbolsGeometry and TopologyDaniell integral28A25Borel measureAnalysisMathematicsReal Analysis Exchange
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Recovering a variable exponent

2021

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.

non-standard growthvariable exponentelliptic equationGeneral Mathematicsquasilinear equationinversio-ongelmatCalderón's problemMathematics - Analysis of PDEsapproximation by polynomialsFOS: Mathematics34A55 (Primary) 41A10 34B15 28A25 (Secondary)inverse problemapproksimointiMüntz-Szász theoremdifferentiaaliyhtälötAnalysis of PDEs (math.AP)Documenta Mathematica
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