A Cantor regular set which does not have Markov's property
A Carleman function and the Cauchy problem for the Laplace equation.
A conforming finite element method with Lagrange multipliers for the biharmonic problem
A Conjugate Gradient Method and a Multigrid Algorithm for Morley' s Finite Element Approximation of the Biharmonic Equation.
A criterion for subharmonicity of a function of the spectrum
A direct method for boundary integral equations on a contour with a peak.
A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
A fast solver for the first biharmonic boundary value problem.
A free boundary problem related to single-layer potentials.
A free boundary value problem in potential theory
This paper is devoted to the formulation and solution of a free boundary problem for the Poisson equation in the plane. The object is to seek a domain and a function defined in satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of . The Neumann data are given in a manner which permits reformulation of the problem as a variational inequality. Under suitable hypotheses about the given data, it is shown that there exists a unique solution...
A general theory of integral transforms and its applications
A generalization of the Phragmén-Lindelöf principle for elliptic differential equations.
A Geometric Property of Functions Harminic in a Disk.
A Hardy space related to the square root of the Poisson kernel
A real-valued Hardy space related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to , and no Orlicz space...
A heat approximation
The Fourier problem on planar domains with time variable boundary is considered using integral equations. A simple numerical method for the integral equation is described and the convergence of the method is proved. It is shown how to approximate the solution of the Fourier problem and how to estimate the error. A numerical example is given.
A mixed finite element method for the biharmonic problem
A mixed-Lagrange multiplier finite element method for the polyharmonic equation
A Multilevel Algorithm for the Biharmonic Problem.
A new class of harmonic multivalent functions defined by an integral operator.
A new setting for potential theory. I
We consider a transient Hunt process in which the potential density satisfies the conditions: (a) for each , is finite continuous in ; (b) iff . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).