A PRIORI INEQUALITIES AND POINTWISE BOUNDS FOR SOLUTION OF CERTAIN ELLIPTIC AND PARABOLIC BOUNDARY VALUE PROBLEMS.
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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In this paper a method of Bramble and Payne is used to obtain a priori pointwise bounds at interior points for the solution of i the Dirichlet problem for a rather general second order nonlinear parabolic operator ii the first boundary value problem for certain linear fourth order elliptic operators and iii the first initialboundary value problem for certain linear fourth order parabolic operators. In addition, a priori bounds for the energy integrals corresponding to the fourth order elliptic operators are derived. Since the bounds obtained are in terms of L2 integrals of the data and, for the fourth order operators, derivatives of the data the Rayleigh-Ritz technique may be employed in the linear problems to obtain close bounds.
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