Infinite dimension of solutions of the Dirichlet problem

• Autorzy: Vladimir Ryazanov
• Języki publikacji: EN

Abstrakty

EN

It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

Słowa kluczowe

EN

Dirichlet problem; Harmonic functions; Laplace equation; Riemann-Hilbert problem

Kategorie tematyczne

• 35F45: Boundary value problems for linear first-order systems
• 34M50: Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
• 31B25: Boundary behavior
• 31A25: Boundary value and inverse problems
• 35Q15: Riemann-Hilbert problems
• 31A05: Harmonic, subharmonic, superharmonic functions
• 31C05: Harmonic, subharmonic, superharmonic functions
• 30E25: Boundary value problems
• 31A20: Boundary behavior (theorems of Fatou type, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

zaakceptowano

2014-05-10

otrzymano

2014-10-29

online

2015-05-20

Twórcy

autor

Vladimir Ryazanov

• Institute of Applied Mathematics and Mechanics, National Academy of Sciences
  of Ukraine, 74 Roze Luxemburg Str., 83114, Donetsk, Ukraine

Bibliografia

• [1] Dovgoshey O., Martio O., Ryazanov V., Vuorinen M. The Cantor function, Expo. Math., 2006, 24, 1-37
• [2] Efimushkin A., Ryazanov V. On the Riemann-Hilbert problem for the Beltrami equations, Contemporary Mathematics (to appear), see also preprint http://arxiv.org/abs/1402.1111v3 [math.CV] 30 July 2014, 1-25
• [3] Garnett J.B., Marshall D.E. Harmonic Measure, Cambridge Univ. Press, Cambridge, 2005
• [4] Gehring F.W., On the Dirichlet problem, Michigan Math. J., 1955-1956, 3, 201
• [5] Goluzin G.M., Geometric theory of functions of a complex variable, Transl. of Math. Monographs, 26, American Mathematical Society, Providence, R.I., 1969
• [6] Koosis P., Introduction to Hp spaces, 2nd ed., Cambridge Tracts in Mathematics, 115, Cambridge Univ. Press, Cambridge, 1998
• [7] Ryazanov V., On the Riemann-Hilbert Problem without Index, Ann. Univ. Bucharest, Ser. Math. 2014, 5, 169-178

Identyfikatory

DOI

10.1515/math-2015-0034