Applications of the implicit function theorem to quasilinear elliptic boundary value problems with non-smooth data
- Universitaet zu Berlin (Germany)
In this paper we consider boundary value problems for systems of quasilinear elliptic equations of the type {minus}{partial_derivative}{sub j}[a{sub ija{beta}}(x, u, {lambda}){partial_derivative}{sub i}u{sub a} + b{sub j{beta}}(x, u, {lambda})]++c{sub ia{beta}}(x, u, {lambda}){partial_derivative}{sub i}u{sub a} + d{sub {beta}}(x, u, {lambda}) = {integral}{beta}. In (1.1) (and in the sequel) the summation over the repeated subscripts i,j = 1, ..., N and a = 1,...,n is understood, and the {open_quotes}free{close_quotes} subscript {beta} varies from 1 to n. The independent variable x = (x{sub 1},...,x{sub N}) belongs to a bounded open domain {Omega} {contained_in} IR{sup N}, and {partial_derivative}{sub i} denotes the partial derivative with respect to x{sub i}. The unknown function u = (u{sub 1},...,u{sub n}) maps {Omega} into IR{sup n}. For the system (1.1) we consider mixed boundary conditions: [a{sub ija{beta}}(x,u,{lambda}){partial_derivative}{sub i}u{sub a} + b{sub j{beta}}(x,u,{lambda})]{nu}{sub j} = g{sub {beta}} for x {epsilon} {Gamma} u{sub {beta}} = h{sub {beta}} for x {epsilon} {partial_derivative}{Omega}/{Gamma}. 16 refs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 482445
- Journal Information:
- Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 9-10 Vol. 20; ISSN 0360-5302; ISSN CPDIDZ
- Country of Publication:
- United States
- Language:
- English
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