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  • 1
    Monograph available for loan
    Monograph available for loan
    Vol. 1 : Incompressible models; 1 (1996)
    Oxford : Clarendon Press
    Associated volumes
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    Call number: PIK M 370-00-0027
    In: Mathematical topics in fluid mechanics
    Type of Medium: Monograph available for loan
    Pages: xiv, 237 S.
    ISBN: 0198514883
    Location: A 18 - must be ordered
    Branch Library: PIK Library
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  • 2
    Monograph available for loan
    Monograph available for loan
    Vol. 2 : compressible models; 2 (1998)
    Oxford : Clarendon Press
    Associated volumes
    Details Availability
    Call number: M 99.0269 ; PIK M 370-00-0028
    In: Mathematical topics in fluid mechanics
    Type of Medium: Monograph available for loan
    Pages: xiv, 348 S.
    ISBN: 0198514883
    Classification:
    C.5.2.
    Location: Upper compact magazine
    Location: A 18 - must be ordered
    Branch Library: GFZ Library
    Branch Library: PIK Library
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  • 3
    Electronic Resource
    Electronic Resource
    Image recovery via total variation minimization and related problems (1997)
    Springer
    Numerische Mathematik 76 (1997), S. 167-188 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):68U10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We study here a classical image denoising technique introduced by L. Rudin and S. Osher a few years ago, namely the constrained minimization of the total variation (TV) of the image. First, we give results of existence and uniqueness and prove the link between the constrained minimization problem and the minimization of an associated Lagrangian functional. Then we describe a relaxation method for computing the solution, and give a proof of convergence. After this, we explain why the TV-based model is well suited to the recovery of some images and not of others. We eventually propose an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals. We propose for instance a variant of the original TV minimization problem that handles correctly some situations where TV fails.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050258
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  • 4
    Electronic Resource
    Electronic Resource
    Convergent difference schemes for nonlinear parabolic equations and mean curvature motion (1996)
    Springer
    Numerische Mathematik 75 (1996), S. 17-41 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 35A40, 35K55, 65M06, 65M12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Explicit finite difference schemes are given for a collection of parabolic equations which may have all of the following complex features: degeneracy, quasilinearity, full nonlinearity, and singularities. In particular, the equation of “motion by mean curvature” is included. The schemes are monotone and consistent, so that convergence is guaranteed by the general theory of approximation of viscosity solutions of fully nonlinear problems. In addition, an intriguing new type of nonlocal problem is analyzed which is related to the schemes, and another very different sort of approximation is presented as well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050228
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  • 5
    Electronic Resource
    Electronic Resource
    Axioms and fundamental equations of image processing (1993)
    Springer
    Archive for rational mechanics and analysis 123 (1993), S. 199-257 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Image-processing transforms must satisfy a list of formal requirements. We discuss these requirements and classify them into three categories: “architectural requirements” like locality, recursivity and causality in the scale space, “stability requirements” like the comparison principle and “morphological requirements”, which correspond to shape-preserving properties (rotation invariance, scale invariance, etc.). A complete classification is given of all image multiscale transforms satisfying these requirements. This classification yields a characterization of all classical models and includes new ones, which all are partial differential equations. The new models we introduce have more invariance properties than all the previously known models and in particular have a projection invariance essential for shape recognition. Numerical experiments are presented and compared. The same method is applied to the multiscale analysis of movies. By introducing a property of Galilean invariance, we find a single multiscale morphological model for movie analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00375127
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  • 6
    Electronic Resource
    Electronic Resource
    Maximal solutions and universal bounds for some partial differential equations of evolution (1989)
    Springer
    Archive for rational mechanics and analysis 105 (1989), S. 163-190 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250835
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  • 7
    Electronic Resource
    Electronic Resource
    Sur les equations de Monge-Ampère (1985)
    Springer
    Archive for rational mechanics and analysis 89 (1985), S. 93-122 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00282327
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  • 8
    Electronic Resource
    Electronic Resource
    Applications of Malliavin calculus to Monte Carlo methods in finance (1999)
    Springer
    Finance and stochastics 3 (1999), S. 391-412 
    Details
    ISSN: 1432-1122
    Keywords: Key words:Monte Carlo methods, Malliavin calculus, hedge ratios and Greeks ; JEL classification :G13 ; Mathematics Subject Classification (1991):60H07, 60J60, 65C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the Malliavin calculus. The Greeks formulae, both with respect to initial conditions and for smooth perturbations of the local volatility, are provided for general discontinuous path-dependent payoff functionals of multidimensional diffusion processes. We illustrate the results by applying the formula to exotic European options in the framework of the Black and Scholes model. Our method is compared to the Monte Carlo finite difference approach and turns out to be very efficient in the case of discontinuous payoff functionals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007800050068
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  • 9
    Electronic Resource
    Electronic Resource
    Boundary regularity for some nonlinear elliptic degenerate equations (1979)
    Springer
    Communications in mathematical physics 70 (1979), S. 181-185 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the nonlinear elliptic degenerate equation (1) $$ - x^2 \left( {\frac{{\partial ^2 u}}{{\partial x^2 }} + \frac{{\partial ^2 u}}{{\partial y^2 }}} \right) + 2u = f(u)in\Omega _a ,$$ where $$\Omega _a = \left\{ {(x,y) \in \mathbb{R}^2 ,0〈 x〈 a,\left| y \right|〈 a} \right\}$$ for some constanta〉0 andf is aC ∞ functions on ℝ such thatf(0)=f′(0)=0. Our main result asserts that: ifu∈C $$(\bar \Omega _a )$$ satisfies (2) $$u(0,y) = 0for\left| y \right|〈 a,$$ thenx −2 u(x,y)∈C ∞ $$\left( {\bar \Omega _{a/2} } \right)$$ and in particularu∈C ∞ $$\left( {\bar \Omega _{a/2} } \right)$$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01982354
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  • 10
    Electronic Resource
    Electronic Resource
    Sur les equations de Monge-Ampere. I (1983)
    Springer
    Manuscripta mathematica 41 (1983), S. 1-43 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we study the real Monge-Arapère equations: det(D2u)= f(x) in 0, u convex in 0, u=0 on ∂0, and we introduce a new method for solving these equations which enables us to show the existence of regular solutions. This method uses only p.d.e. techniques and does not use any geometrical results. Furthermore, it enables us to solve quasilinear Monge-Ampère equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01165928
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