Search results for "Inverse function theorem"

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Infinite Dimensional Banach spaces of functions with nonlinear properties

2010

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R(n) failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Inverse function theoremMathematics::Functional AnalysisMathematics(all)Approximation propertyGeneral MathematicsMathematical analysisInfinite-dimensional vector functionEberlein–Šmulian theoremBanach manifold/dk/atira/pure/subjectarea/asjc/2600Interpolation spaceLp spaceC0-semigroupMathematics
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Invertibility of Sobolev mappings under minimal hypotheses

2010

Abstract We prove a version of the Inverse Function Theorem for continuous weakly differentiable mappings. Namely, a nonconstant W 1 , n mapping is a local homeomorphism if it has integrable inner distortion function and satisfies a certain differential inclusion. The integrability assumption is shown to be optimal.

Sobolev spaceInverse function theoremDiscrete mathematicsDistortion functionDifferential inclusionIntegrable systemApplied MathematicsLocal homeomorphismDifferentiable functionHomeomorphismMathematical PhysicsAnalysisMathematicsAnnales de l'Institut Henri Poincare (C) Non Linear Analysis
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