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A hypercomplex method for solving piecewise continuous biharmonic problem in domains with corner points

S. V. Gryshchuk, S. A. Plaksa

Abstract

A piecewise continuous biharmonic problem in domains with corner points and a corresponding Schwarz type boundary value problem for monogenic functions in a commutative biharmonic algebra are considered. A method for reducing the problems to a system of integral equations is developed.

A hypercomplex method for solving piecewise continuous biharmonic problem in domains with corner points

Abstract

A piecewise continuous biharmonic problem in domains with corner points and a corresponding Schwarz type boundary value problem for monogenic functions in a commutative biharmonic algebra are considered. A method for reducing the problems to a system of integral equations is developed.

Paper Structure

This paper contains 12 theorems, 211 equations.

Key Result

lemma 1

Нехай функція $\Omega \colon \left(\Gamma \setminus \mathcal{X}\right) \times \left(\overline{\mathcal{U}} \setminus \mathcal{X} \right) \longrightarrow \mathbb{C}$ задовольняє оцінки де стала $c$ не залежить від $S$, $Z$, $T$, $Z_0$; $\beta \in (0; 1)\emph{;} \, \beta_0 \ge 0$; $\omega_k \colon (0; +\infty) \longrightarrow (0; +\infty)$ при $k=0,1,2$ --- неспадні обмежені функції, які задовольня

Theorems & Definitions (12)

  • lemma 1
  • lemma 2
  • lemma 3
  • lemma 4
  • lemma 5
  • lemma 6
  • lemma 7
  • lemma 8
  • lemma 9
  • lemma 10
  • ...and 2 more