Browsing by Subject "Dirichlet problem"

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    Dirichlet problem for polynomials on the unit disk
    (Korean Mathematical Society, 2014) Sertöz, A. S.
    We give explicit formulas, without using the Poisson integral, for the functions that are C-harmonic on the unit disk and restrict to a prescribed polynomial on the boundary. © 2014 Korean Mathematical Society.
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    Triplets of closely embedded Hilbert spaces
    (Springer, 2014) Cojuhari, P.; Gheondea, A.
    We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. We provide a model and an abstract theorem as well for a triplet of closely embedded Hilbert spaces associated to positive selfadjoint operator H, that is called the Hamiltonian of the system, which is supposed to be one-to-one but may not have a bounded inverse. Existence and uniqueness results, as well as left-right symmetry, for these triplets of closely embedded Hilbert spaces are obtained. We motivate this abstract theory by a diversity of problems coming from homogeneous or weighted Sobolev spaces, Hilbert spaces of holomorphic functions, and weighted L2 spaces. An application to weak solutions for a Dirichlet problem associated to a class of degenerate elliptic partial differential equations is presented. In this way, we propose a general method of proving the existence of weak solutions that avoids coercivity conditions and Poincaré–Sobolev type inequalities. © 2014, Springer Basel.