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Can I read The Dirichlet Problem for Some Semilinear Elliptic Differential Equations of Arbitrary Order on EtoBox?
The Dirichlet Problem for Some Semilinear Elliptic Differential Equations of Arbitrary Order by Hans-Christoph Granau is a Mathematics article available to read on EtoBox.
What is The Dirichlet Problem for Some Semilinear Elliptic Differential Equations of Arbitrary Order about?
For some special semilinear elliptic equations, e.g. (-A) m u + g(u) = f, the existence of a solution of the Dirichlet problem is shown, which is classical in the interior of the domain and takes on the boundary values in a weak sense. The nonlinearity g : E -» E has to satisfy the sign condition t • g(t) S 0 and to be bounded from below, e.g. g(t) = exp(t) -1. Furthermore it is possible to treat nonlinearities g with growth conditions, which can be viewed as inteipolation between the above extreme case and the standard one lg(t)l < C (l + ltl n+2m/n " 2m ). The crucial lemma is a local maximum principle for solutions of differential inequalities (-A) m u S f, which makes use of the positivity of Green's function for (~A) m in balls.
Who reads The Dirichlet Problem for Some Semilinear Elliptic Differential Equations of Arbitrary Order?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Hans-Christoph Granau
- Published
- 1991
- Language
- EN
- Field
- Mathematics (Physical Sciences)