On a nonlocal problem for the Laplace equation in the unit ball with fractional boundary conditions

Abstract

In this paper, we investigate the correct solvability for the Laplace equation with a nonlocal boundary condition in the unit ball. The considered boundary operator is of fractional order. This problem is a generalization of the well‐known Bitsadze–Samarskii problem. Copyright © 2015 John Wiley & Sons, Ltd.

About solvability of some boundary value problems for poisson equation in the ball

“…Note that the local and nonlocal boundary value problems with boundary operators of fractional order for the second order elliptic equations were studied in [5,7,8,16,17,21] and for higher-order equations in [1-3, 18, 19].…”

On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions

“…Note that the questions about the solvability of the main problems for the nonlocal Poisson equation were studied in [20,21]. Note also that boundary value problems with fractional-order boundary operators for elliptic equations were studied in [22][23][24][25][26][27][28][29][30].…”

On the solvability of some boundary value problems for the Poisson equation

“…Бұл есептердің тарихына шолу жасайтын болсақ, эллипс тектес теңдеулер үшін шекаралық шартында бөлшек ретті оператор қатысқан шеттік есеп алғашқы рет С.Умаровтың [4] жұмысында зерттелінген. Кейін мұндай есептерге көптеген ғалымдардың назары түсті [5][6][7][8][9][10].…”