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)


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


Banach Space Sobolev Space Uniqueness Theorem Monotone Operator Closed Curve 
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    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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