TY - JOUR

T1 - Dirichlet problem for degenerate elliptic equations

AU - Friedman, Avner

AU - Pinsky, Mark A.

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1973/12

Y1 - 1973/12

N2 - Let L0 be a degenerate second order elliptic operator with no zeroth order term in an m-dimensional domain G9 and let L = L0 + c. One divides the boundary of G into disjoint sets ∑1,∑2, ∑3,∑3the non characteristic part, and on ∑2 the "drift” is outward. When c is negative, the following Dirichlet problem has been considered in the literature: Lu =0 in G, u is prescribed on ∑2u ∑3. In the present work it is assume that c ≤ 0. Assuming additional boundary conditions on a certain finite number of points of ∑1, a unique solution of the Dirichlet problem is established.

AB - Let L0 be a degenerate second order elliptic operator with no zeroth order term in an m-dimensional domain G9 and let L = L0 + c. One divides the boundary of G into disjoint sets ∑1,∑2, ∑3,∑3the non characteristic part, and on ∑2 the "drift” is outward. When c is negative, the following Dirichlet problem has been considered in the literature: Lu =0 in G, u is prescribed on ∑2u ∑3. In the present work it is assume that c ≤ 0. Assuming additional boundary conditions on a certain finite number of points of ∑1, a unique solution of the Dirichlet problem is established.

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U2 - 10.1090/S0002-9947-1973-0328345-2

DO - 10.1090/S0002-9947-1973-0328345-2

M3 - Article

AN - SCOPUS:84966246825

SN - 0002-9947

VL - 186

SP - 359

EP - 383

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

ER -