116 research outputs found
Boundedness of the gradient of a solution to the Neumann-Laplace problem in a convex domain
It is shown that solutions of the Neumann problem for the Poisson equation in
an arbitrary convex -dimensional domain are uniformly Lipschitz.
Applications of this result to some aspects of regularity of solutions to the
Neumann problem on convex polyhedra are given
Criteria for the -dissipativity of systems of second order differential equations
We give complete algebraic characterizations of the -dissipativity of
the Dirichlet problem for some systems of partial differential operators of the
form , were are matrices. First, we determine the sharp angle of
dissipativity for a general scalar operator with complex coefficients. Next we
prove that the two-dimensional elasticity operator is -dissipative if
and only if
being the Poisson ratio. Finally we find a necessary and sufficient
algebraic condition for the -dissipativity of the operator , where are
matrices with complex entries, and we describe the maximum
angle of -dissipativity for this operator.Comment: 42 pages, LaTeX, no figure
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