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  • 1
    Electronic Resource
    Electronic Resource
    Some overdetermined boundary value problems for harmonic functions (1991)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 42 (1991), S. 864-873 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Cet article est consacré à l'étude de certains problèmes surdéterminés pour des fonctions harmoniques. En particulier, nous montrons que si le gradient de la seconde fonction propre du problème de Stekloff défini dans un domaine Ω borné, simplement connexe du plan, a son module constant sur la frontière ∂Ω, alors Ω est nécessairement un disque.
    Notes: Summary In this paper we study various overdetermined problems involving harmonic functions. In particular, we show that if the second eigenfunctionu 2 of the Stekloff eigenvalue problem in a bounded simply connected plane domain Ω has a constant value of ∥∂u 2∥ on ∇Ω, then Ω is a disk
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944568
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder (1992)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 405-421 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Various, but closely related, forms of a Phragmén-Lindelöf principle are established for certain classes of semi-linear elliptic equations (including systems) defined on a half-cylinder. For example, it is shown that under either homogeneous Dirichlet or Neumann lateral boundary conditions, the smooth solution either fails to exist globally, or when it does exist globally it must tend asymptotically to zero with increasingly large distance along the cylinder from the base. For uniformly elliptic equations, the decay to zero is at least exponential. The method employed relies upon cross-sectional estimates and is additionally applicable to both the finite and whole cylinder. In the latter case, global existence fails for all non-trivial solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946237
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Some Phragmén-Lindelöf type results for the biharmonic equation (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 414-432 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wir leiten Abschätzungen für gewichtete und ungewichtete Energieausdrücke für die Lösung einer biharmonischen Randwertaufgabe in der Ebene mittels einer zweite Ordnung Differentialungleichung ab. Wir betrachten drei Arten von unbeschränkten Gebieten mit Randbedingungen des Dirichletschen Typs. Für jedes Gebiet entwickeln wir exponential Abschätzungen mit entweder positivem oder negativem Wachstum. Im Falle des negativem Wachstums geben wir auch eine Methode an, um explizite Abschätzungen für die totale Energie zu erhalten.
    Notes: Abstract We derive estimates for weighted and unweighted energy expressions for the solution of a biharmonic boundary value problem in the plane by means of a second order differential inequality. We consider three kinds of unbounded domains with boundary conditions of Dirichlet type. For each domain we develop exponential estimates that either grow or decay. In the case of decay we also present a method for obtaining explicit bounds for the total energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945929
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  • 4
    Electronic Resource
    Electronic Resource
    Phragmén-Lindelöf and continuous dependence type results in generalized heat conduction (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 527-538 
    Details
    ISSN: 1420-9039
    Keywords: 35K50 ; 35B20 ; 35B30 ; 35B40 ; Heat conduction ; continuous dependence ; decay estimate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using an energy method we investigate the decay of end effects for a generalized heat conduction problem defined on a semi-infinite cylindrical region. With homogeneous Dirichlet conditions on the lateral surface of the cylinder it is shown that solutions either grow exponentially or decay exponentially in the distance from the finite end of the cylinder. The effect of perturbing the equation parameters is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00914869
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Upper and lower bounds in equations of forced vibration type (1963)
    Springer
    Archive for rational mechanics and analysis 14 (1963), S. 153-170 
    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/BF00250697
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  • 6
    Electronic Resource
    Electronic Resource
    Phragmén-lindelöf type results for harmonic functions with nonlinear boundary conditions (1993)
    Springer
    Archive for rational mechanics and analysis 122 (1993), S. 123-144 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper is concerned with investigating the asymptotic behavior of harmonic functions defined on a three-dimensional semi-infinite cylinder, where homogeneous nonlinear boundary conditions are imposed on the lateral surface of the cylinder. Such problems arise in the theory of steady-state heat conduction. The classical Phragmén-Lindelöf theorem states that harmonic functions which vanish on the lateral surface of the cylinder must either grow exponentially or decay exponentially with distance from the finite end of the cylinder. Here we show that the results are significantly different when the homogeneous Dirichlet boundary condition is replaced by the nonlinear heatloss or heat-gain type boundary condition. We show that polynomial growth (or decay) or exponential growth (or decay) may occur, depending on the form of the nonlinearity. Explicit estimates for the growth or decay rates are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00378164
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  • 7
    Electronic Resource
    Electronic Resource
    On the asymptotic behavior of solutions of linear second-order boundary-value problems on a semi-infinite strip (1993)
    Springer
    Archive for rational mechanics and analysis 124 (1993), S. 277-303 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper treats the asymptotic behavior of solutions of a linear secondorder elliptic partial differential equation defined on a two-dimensional semiinfinite strip. The equation has divergence form and variable coefficients. Such equations arise in the theory of steady-state heat conduction for inhomogeneous anisotropic materials, as well as in the theory of anti-plane shear deformations for a linearized inhomogeneous anisotropic elastic solid. Solutions of such equations that vanish on the long sides of the strip are shown to satisfy a theorem of Phragmén-Lindelöf type, providing estimates for the rate of growth or decay which are optimal for the case of constant coefficients. The results are illustrated by several examples. The estimates obtained in this paper can be used to assess the influence of inhomogeneity and anisotropy on the decay of end effects arising in connection with Saint-Venant's principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00953070
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Bounds in the Cauchy problem for the Laplace equation (1960)
    Springer
    Archive for rational mechanics and analysis 5 (1960), S. 35-45 
    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/BF00252897
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  • 9
    Electronic Resource
    Electronic Resource
    Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics (1971)
    Springer
    Archive for rational mechanics and analysis 41 (1971), S. 363-398 
    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/BF00281873
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  • 10
    Electronic Resource
    Electronic Resource
    On Korn's inequality (1961)
    Springer
    Archive for rational mechanics and analysis 8 (1961), S. 89-98 
    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/BF00277432
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