Search results for "Comparison result"

showing 9 items of 9 documents

Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting

2018

We show existence of a unique solution and a comparison theorem for a one-dimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a time-dependent extended monotonicity condition in the y-variable and have linear time-dependent growth. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008) and, in the $L^2$-case with linear growth, those of Kruse and Popier (2016). Moreover, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we consider BSDEs where the Poisson random measure admits only jumps of size larger than $1/n$. We show con…

Comparison theorembackward stochastic differential equationMonotonic function01 natural sciencesLévy processlcsh:QA75.5-76.95010104 statistics & probabilityMathematics::ProbabilityApplied mathematicsUniqueness0101 mathematicsBrownian motionstokastiset prosessitMathematicsLévy processResearch010102 general mathematicsComparison resultsPoisson random measureBackward stochastic differential equationlcsh:Electronic computers. Computer science60H10lcsh:Probabilities. Mathematical statisticscomparison theoremlcsh:QA273-280differentiaaliyhtälötMathematics - ProbabilityGenerator (mathematics)existence and uniquenessProbability, Uncertainty and Quantitative Risk
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Symmetrization for singular semilinear elliptic equations

2012

In this paper, we prove some comparison results for the solution to a Dirichlet problem associated with a singular elliptic equation and we study how the summability of such a solution varies depending on the summability of the datum f. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.

Dirichlet problemSharp a priori estimatesSemilinear elliptic equationsMathematics::Operator AlgebrasApplied MathematicsMathematical analysisMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEsComparison resultsSymmetrizationGeodetic datumElliptic curveSettore MAT/05 - Analisi MatematicaMathematics::K-Theory and HomologySymmetrizationMathematics
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Comparison results for Hessian equations via symmetrization

2007

where the λ’s are the eigenvalues of the Hessian matrix D2u of u and Sk is the kth elementary symmetric function. For example, for k = 1, S1(Du) = 1u, while, for k = n, Sn(D 2u) = detD2u. Equations involving these operators, and some more general equations of the form F(λ1, . . . , λn) = f in , (1.2) have been widely studied by many authors, who restrict their considerations to convenient cones of solutions with respect to which the operator in (1.2) is elliptic. Following [25] we define the cone 0k of ellipticity for (1.1) to be the connected component containing the positive cone 0 = {λ ∈ R : λi > 0 ∀i = 1, . . . , n} of the set where Sk is positive. Thus 0k is an open, convex, symmetric…

Hessian matrixHessian equationsymmetrizationHessian operatorApplied MathematicsGeneral Mathematicscomparison resultHessian equationCombinatoricssymbols.namesakeOperator (computer programming)Cone (topology)Settore MAT/05 - Analisi MatematicaVertex (curve)symbolsSymmetrizationElementary symmetric polynomialMoser type inequalitiesAlgorithmEigenvalues and eigenvectorsMathematics
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Full-parallax immersive 3D display from depth-map cameras

2016

We exploit two different versions of the Kinect to make comparison of three-dimensional (3D) scenes displayed by proposed integral imaging (InI) display system. We attempt to show the difference between each version specifications and capacity. Furthermore, we illustrate our study result with some empirical imaging experiment in which the final result are displayed with full-parallax. Each demonstrated integral images can provide clear comparison results to the observer.

Integral imagingComputer sciencebusiness.industryComparison results02 engineering and technologyObserver (special relativity)Stereo display01 natural sciences010309 opticsDepth mapComputer graphics (images)0103 physical sciences0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingComputer visionArtificial intelligencebusinessParallax2016 15th Workshop on Information Optics (WIO)
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A symmetrization result for Monge–Ampère type equations

2007

In this paper we prove some comparison results for Monge–Ampere type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematics::Complex VariablesGeneral MathematicsMathematical analysisComparison resultsMonge-Ampère equationEigenfunctionType (model theory)Monge-Ampère equationsDimension (vector space)Settore MAT/05 - Analisi Matematicaeigenvalue problemrearrangementsSymmetrizationAmpereEigenvalue problemsMathematicsMathematische Nachrichten
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On a time-depending Monge-Ampère type equation

2012

Abstract In this paper, we prove a comparison result between a solution u ( x , t ) , x ∈ Ω ⊂ R 2 , t ∈ ( 0 , T ) , of a time depending equation involving the Monge–Ampere operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g ( x , t ) over sublevel sets of u , { x ∈ Ω : u ( x , t ) ϑ } , ϑ ∈ R , having the same perimeter in R 2 .

Pure mathematicsDerivation formulaPlane (geometry)Applied MathematicsOperator (physics)Mathematical analysisComparison resultsSymmetrizationMonge-Ampère equationType equationSettore MAT/05 - Analisi MatematicaAmpereAnalysisMathematics
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Comparison results for Monge - Ampère type equations with lower order terms

2003

In this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems.

RearrangementsMathematics::Complex VariablesIndependent equationApplied MathematicsMathematical analysisMathematics::Analysis of PDEsComparison resultsSymmetrizationLower orderType (model theory)Monge-Ampère equationsPerimeterSettore MAT/05 - Analisi MatematicaSimultaneous equationsFully nonlinear elliptic equationsSymmetrizationAmpereAnalysisMathematics
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A comparison result for a class of semilinear elliptic equations

1997

Comparison results

Settore MAT/05 - Analisi MatematicaComparison results
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Comparison results for a linear elliptic equation with mixed boundary conditions

2003

In this paper we study a linear elliptic equation having mixed boundary conditions, defined in a connected open set $\Omega $ of $\mathbb{R}^{n}$. We prove a comparison result with a suitable ``symmetrized'' Dirichlet problem which cannot be uniformly elliptic depending on the regularity of $ \partial \Omega $. Regularity results for non-uniformly elliptic equations are also given.

symmetrization35B6535J25Settore MAT/05 - Analisi MatematicaApplied Mathematics35B05Comparison result35J70Analysis
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