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On the Strong Solvability of a Unilateral Boundary Value Problem for Nonlinear Parabolic Operators in the Plane

  • Rosalba Di Vincenzo
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 68)

Abstract

In this paper we study the strong solvability of the following boundary value problem with unilateral boundary conditions
$$\left\{ {\begin{array}{*{20}{c}} {\mathcal{A}(X,H(u)) - \frac{{\partial u}}{{\partial t}} = f(X)} \hfill & {a.e. in Q = \Omega \times ]0,T[} \hfill \\ {u(x,0) = 0} \hfill & {in \Omega } \hfill \\ {u \geqslant 0,\frac{{\partial u}}{{\partial n}} \geqslant 0, u \cdot \frac{{\partial u}}{{\partial n}} = 0} \hfill & {on\partial \Omega \times ]0,T[,} \hfill \\ \end{array} } \right.$$
(1)
where n is the unit outward normal to the boundary of Ω, ∂Ω.

Keywords

Banach Space Sobolev Space Uniqueness Theorem Monotone Operator Closed Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. Brezis, “Problèmes Unilatéraux”J. Math. Pures et Appl. 51, Fasc 1 (1972), pp. 1–168.MathSciNetGoogle Scholar
  2. [2]
    S. Campanato, “On the condition of nearness between operators”, Ann. Mat. Pura Appl., 167(1994), pp. 243–256.MathSciNetCrossRefGoogle Scholar
  3. [3]
    S. Giuffrè, “On the strong solvability of a unilateral boundary value problem for nonlinear discontinuous operators in the plane”, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, Kluwer Academic Publishers, F. Giannessi A. Maugeri P. Pardalos Eds., 2001.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Rosalba Di Vincenzo
    • 1
  1. 1.Dipartimento di MatematicaUniversità di CataniaCataniaItalia

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