• Corpus ID: 235293736

On Dirichlet problem for second-order elliptic equations in the plane and uniform approximation problems for solutions of such equations

@inproceedings{Bagapsh2021OnDP,
  title={On Dirichlet problem for second-order elliptic equations in the plane and uniform approximation problems for solutions of such equations},
  author={Astamur Bagapsh and Konstantin Yu. Fedorovskiy and Maksim Ya Mazalov},
  year={2021}
}
We consider the Dirichlet problem for solutions to general second-order homogeneous elliptic equations with constant complex coefficients. We prove that any Jordan domain with C-smooth boundary, 0 < α < 1, is not regular with respect to the Dirichlet problem for any not strongly elliptic equation Lf = 0 of this kind, which means that for any such domain G it always exists a continuous function on the boundary of G that can not be continuously extended to the domain under consideration to a… 

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References

SHOWING 1-10 OF 62 REFERENCES
Uniform approximation by polynomial solutions of second-order elliptic equations, and the corresponding Dirichlet problem
Conditions for the uniform approximability of functions by polynomial solutions of second-order elliptic equations with constant complex coefficients on compact sets of special form in ℝ2 are
On the uniform approximation problem for the square of the Cauchy-Riemann operator
Let X be a compact subset of the plane and / a continuous function on X satisfying the equation d / = 0 in the interior of X. It is unknown whether / can be uniformly approximated on X by functions g
Uniform approximability of functions by polynomial solutions of second-order elliptic equations on compact plane sets
We investigate conditions for the uniform approximability of functions by polynomial solutions of second-order elliptic equations with constant complex coefficients on compact sets in . Some new
Analysis on Real and Complex Manifolds
Chapters: 1. Differentiable Functions in Rn. Taylor's Formula. Partitions of Unity. Inverse Functions, Implicit Functions and the Rank Theorem. Sard's Theorem and Functional Dependence. Borel's
Boundary regularity of Nevanlinna domains and univalent functions in model subspaces
In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains
The Dirichlet problem for polyanalytic functions
Connections between the boundary behaviour of polyanalytic functions and the structure of the boundary are investigated. In particular, a Jordan domain with Lipschitz boundary is constructed which is
Boundary values of continuous analytic functions
Let U, K, and C denote the open unit disc, the closed unit disc, and the unit circumference, respectively. Let A be the set of all complex-valued functions which are defined and continuous on K and
On uniform approximation by polyanalytic polynomials and the Dirichlet problem for bianalytic functions
New necessary and sufficient conditions for the uniform approximability of functions by polyanalytic polynomials and polyanalytic rational functions on compact subsets of the plane are established.
The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions
which converges uniformly f or all values of 6. This is of course a general fact, tha t if a given function can be uniformly approximated as closely as desired by a linear combination of other
Nevanlinna domains with large boundaries
Abstract Nevanlinna domains are an important class of bounded simply connected domains in the complex plane; they are images of the unit disc under mappings by univalent functions belonging to model
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