On boundary value problems of neumann type for the dirac operator in a half space of

1993 ◽  
Vol 23 (1-2) ◽  
pp. 1-16 ◽  
Author(s):  
Chiping Zhou
Keyword(s):  
Dirac Operator ◽  
Boundary Value Problems ◽  
Half Space ◽  
Boundary Value ◽  
Neumann Type

scholarly journals Polyanalytic boundary value problems for planar domains with harmonic Green function

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Heinrich Begehr ◽  
Bibinur Shupeyeva
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Planar Domains ◽  
Schwarz Problem ◽  
Bianalytic Functions ◽  
Neumann Type ◽  
The Neumann Problem ◽  
Well Posed

AbstractThere are three basic boundary value problems for the inhomogeneous polyanalytic equation in planar domains, the well-posed iterated Schwarz problem, and further two over-determined iterated problems of Dirichlet and Neumann type. These problems are investigated in planar domains having a harmonic Green function. For the Schwarz problem, treated earlier [Ü. Aksoy, H. Begehr, A.O. Çelebi, AV Bitsadze’s observation on bianalytic functions and the Schwarz problem. Complex Var Elliptic Equ 64(8): 1257–1274 (2019)], just a modification is mentioned. While the Dirichlet problem is completely discussed for arbitrary order, the Neumann problem is just handled for order up to three. But a generalization to arbitrary order is likely.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

scholarly journals On the Boundary Value Problems of Circular Loading for Transversely Isotropic Piezoelectric Half Space.

2001 ◽  
Vol 44 (4) ◽  
pp. 462-471 ◽  
Author(s):  
IGN Wiratmaja PUJA ◽  
Toshikazu SHIBUYA ◽  
Kikuo KISHIMOTO ◽  
Hirotsugu INOUE
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Boundary Value ◽  
Transversely Isotropic

Iterative bounds for the stable solutions of convex non-linear boundary value problems

1977 ◽  
Vol 76 (2) ◽  
pp. 81-94 ◽  
Author(s):  
J. W. Mooney ◽  
G. F. Roach
Keyword(s):  
Boundary Value Problems ◽  
Differential Expression ◽  
Boundary Value ◽  
Linear Boundary ◽  
Non Linear ◽  
Unstable Solutions ◽  
Neumann Type ◽  
Thermal Combustion ◽  
Stable Solutions ◽  
Image Position

SynopsisWe consider a class of convex non-linear boundary value problems of the formwhere L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.

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