Search results for " Semicontinuity"

showing 3 items of 3 documents

Lower semicontinuity of weak supersolutions to the porous medium equation

2013

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero. This shows that weak supersolutions belong to a class of supersolutions defined by a comparison principle.

Degenerate diffusion35K55 31C45Applied MathematicsGeneral MathematicsMathematical analysista111Mathematics::Analysis of PDEscomparison principlelower semicontinuitysupersolutionsMathematics - Analysis of PDEsporous medium equationFOS: MathematicsPorous mediumdegenerate diffusionSign (mathematics)MathematicsAnalysis of PDEs (math.AP)
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Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Operator AlgebrasSesquilinear formGeneral MathematicsMathematics::Optimization and ControlMathematics::General TopologyClosedness Semicontinuity Sesquilinear formsDomain (mathematical analysis)Topological vector spaceSettore MAT/05 - Analisi MatematicaAlgebra over a fieldCompleteness (statistics)Equivalence (measure theory)Subspace topologyQuotientMathematicsRendiconti del Circolo Matematico di Palermo
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THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE

2014

We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…

Unit spherenonconvex variational problemsriemannian manifolds with boundaryGeodesicn-sphereharmonic flows68U1053C2253C4435K9235K67Neumann boundary conditionpartial differential equations49J45MathematicsNumerical Analysisnonlinear parabolic systems; lower semicontinuity and relaxation; total variation flow; 1-harmonic flow; image processing; harmonic flows; partial differential equations; image processing.; geodesics; riemannian manifolds with boundary; nonconvex variational problemslower semicontinuity and relaxation58E20Applied MathematicsMathematical analysis49Q201-harmonic flowimage processingFlow (mathematics)35K55Metric (mathematics)total variation flowVector fieldnonlinear parabolic systemsBalanced flowAnalysisgeodesics
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