×

An existence and uniqueness theorem for the solution of an elliptic- parabolic inequality with discontinuous coefficients in non-divergence form. (Italian. English summary) Zbl 0569.35021

This paper deals with Dirichlet problems of the type: \[ \sum^{n- 1}_{i=1}a_ i(\partial^ 2u/\partial x^ 2_ i)+c(\partial^ 2u/\partial z^ 2)+q(\partial u/\partial z)+\mu u=f\quad in\quad D\quad where \]
\[ D=(0,1)^{n-1}\times (-1,1),\quad c=z^{2+\sigma}\quad if\quad z\geq 0;\quad c=0\quad elsewhere, \] and u satisfies certain boundary conditions. The author first derives a priori estimates for norms related to the specific form of the problem. He then uses a continuity method to establish the existence of a unique solution for \(\mu\) sufficiently small.
Reviewer: C.Bandle

MSC:

35J25 Boundary value problems for second-order elliptic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35R05 PDEs with low regular coefficients and/or low regular data
35B45 A priori estimates in context of PDEs
PDFBibTeX XMLCite