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A homogeneous Dirichlet problem for a nonlinear partial differential equation in an anisotropic Sobolev space. (English) Zbl 0652.47033
The author solves a homogeneous Dirichlet problem for a quasilinear partial differential operator by showing that under certain conditions this operator generates a coercive pseudo-monotone operator from an appropriate anisotropic Sobolev space onto its dual.
Reviewer: Simeon Reich
MSC:
47H05 Monotone operators and generalizations
47F05 General theory of partial differential operators
30G30 Other generalizations of analytic functions (including abstract-valued functions)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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