TY - JOUR

T1 - Investigation of a problem for the Laplace equation with a boundary condition of a special form in a plane angle

AU - Solonnikov, V. A.

AU - Frolova, E. V.

PY - 1992/11/1

Y1 - 1992/11/1

N2 - The explicit solution of the equation Δu=f in a plane infinite angle, satisfying on one side of the angle a Neumann condition and on the other one the condition ∂u/∂n + h∂u/∂r + σu=Ψ (∂/∂r is the tangential derivative, σ ε C, ℜσ ≥ 0), is constructed and estimated in weighted Sobolev spaces. The obtained estimates are sharp with respect to the differential order and are uniform with respect to σ. The construction of the solution reduces to the investigation of a finite difference equation in the complex plane, arising after a Mellin transform. © 1992 Plenum Publishing Corporation.

AB - The explicit solution of the equation Δu=f in a plane infinite angle, satisfying on one side of the angle a Neumann condition and on the other one the condition ∂u/∂n + h∂u/∂r + σu=Ψ (∂/∂r is the tangential derivative, σ ε C, ℜσ ≥ 0), is constructed and estimated in weighted Sobolev spaces. The obtained estimates are sharp with respect to the differential order and are uniform with respect to σ. The construction of the solution reduces to the investigation of a finite difference equation in the complex plane, arising after a Mellin transform. © 1992 Plenum Publishing Corporation.

UR - http://www.scopus.com/inward/record.url?scp=33747487364&partnerID=8YFLogxK

U2 - 10.1007/BF01671007

DO - 10.1007/BF01671007

M3 - Article

AN - SCOPUS:33747487364

VL - 62

SP - 2819

EP - 2831

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -