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    Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

    By: Vladimir Kondratiev, Michail Borsuk

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    ISBN
    9780080461731
    Date Released
    Binding
    eBook
     
     

    Out of Print

    Description
    The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.

    Key features:
    * New the Hardy - Friedrichs - Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.
    * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
    * The question about the influence of the coefficients smoothness on the regularity of solutions.
    * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
    * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
    * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.
    * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

    * Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
    * The question about the influence of the coefficients smoothness on the regularity of solutions.
    * New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
    * The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
    * The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.
    * The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

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