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Displaying similar documents to “Dirichlet problems for the biharmonic equation.”

Examples of non-local time dependent or parabolic Dirichlet spaces

Niels Jacob (1993)

Colloquium Mathematicae

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In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families ( E ( τ ) ) τ ∈ ℝ of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second...

Some applications of minimax and topological degree to the study of the Dirichlet problem for elliptic partial differential equations

Leszek Gęba, Tadeusz Pruszko (1991)

Annales Polonici Mathematici

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This paper treats nonlinear elliptic boundary value problems of the form (1) L[u] = p(x,u) in Ω ⊂ ℝ n , u = D u = . . . = D m - 1 u on ∂Ω in the Sobolev space W 0 m , 2 ( Ω ) , where L is any selfadjoint strongly elliptic linear differential operator of order 2m. Using both topological degree arguments and minimax methods we obtain existence and multiplicity results for the above problem.