Search results for "harmonic flows"

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Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.

Unit spheren-sphereGeodesicApplied MathematicsMathematical analysisA domainharmonic flowsOctant (solid geometry)non-convex variational problems1-harmonic flowlower semi-continuity and relaxation; total variation flow; 1-harmonic flow; non-convex variational problems; image processing; geodesic; partial differential equations; harmonic flowsimage processingHomogeneoustotal variation flowNeumann boundary conditionJumppartial differential equationslower semi-continuity and relaxationgeodesicMathematics
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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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