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  • 11
    Electronic Resource
    Electronic Resource
    Qualitative properties of the boundary derivative of the capacity potential for special classes of annular domains (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 251-259 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let U(p) denote the capacity potential in an annular domain Ω (bounded by Jordan curves). We describe the qualitative behavior of ∥Δ∥ on the line segments of ∂Ω which are arbitrary, radial, or ν-directional (for some vector ν ≠ 0) in the respective cases where Ω is a convex, starlike, or ≠-convex annular domain. We apply these results to some free-boundary extremal problems in which the capacity plus weighted area functional is minimized in restricted classes of annular domains Ω.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070116
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    Paper (German National Licenses)
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  • 12
    Electronic Resource
    Electronic Resource
    On the geometric form of free boundaries satisfying a bernoulli condition. II (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 387-404 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the x-y plane, let Ω be an annular domain whose interior boundary Γ* is a known Jordan curve and whose exterior boundary Γ is a free boundary characterized by the condition that|ΔU| = 1 on Γ, where U is the capacity potential in Ω. We obtain a qualitative description of Γ involving such things as its inflection points and local maxima and minima relative to specified directions. We also extend these results to obtain qualitative properties of the free boundary when it is subjected to various geometric contraints. Our results generalize those in [1].
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080126
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    Paper (German National Licenses)
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  • 13
    Electronic Resource
    Electronic Resource
    On the geometric form of solutions of a free boundary problem involving galvanization (1987)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 9 (1987), S. 99-104 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In [6], T. I. Vogel studied a free boundary problem originating in the galvanization process. He showed that if the given boundary Γ* is starlike or convex, then so is the free boundary solution Γ. Our purpose is to generalize Vogel's second result by showing (under certain assumptions) that Γ cannot have more (local) maxima or minima (relative to a given direction) than Γ*; also that Γ cannot have more inflection points or greater total curvature than Γ*. The author has already proven analogous results for the Bernoulli free boundary problem in [1], [2] and [3].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670090109
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    Paper (German National Licenses)
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  • 14
    Electronic Resource
    Electronic Resource
    Radial sums of ridge functions: A characterization (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 90-100 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We extend and sharpen the characterization of radial sums of ridge functions of two variables given in an earlier paper. More precisely, a bound on the degree of certain polynomials is given which depends on the angles between the ridges; not only is this bound best possible but also a converse result holds. Furthermore, variants of this characterization which hold for higher dimensional analogues are also given. These results are then applied to certain parallel am models in computed tomography to obtain more precise and otherwise improved characterizations of algorithms which commute with rigid motions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070106
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    Paper (German National Licenses)
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  • 15
    Electronic Resource
    Electronic Resource
    Stabilization and regularization for solutions of an ill posed problem for the wave equation (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 202-209 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we study the problem of finding u: [O, T] → D(A), D(A) ⊆ H, H a Hibert space such that:Is a linear positive, self-adjoint operator with a compact inverse. The problem is well known to be illposed because uniqueness and existence generally fail. We restore the stability with an a priori bound on ∥ du(0)/dt ∥ for some particular values of T.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070112
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    Paper (German National Licenses)
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