Equations of mixed elliptic-hyperbolic type with a homogeneous Dirichlet condition imposed on the entire boundary will be discussed. Such colosed problems are typically overdetermined in spaces of classical solutions in contrast to the well-posedness for classical solutions that can result from opening the boundary by prescribing the boundary condition only on a proper subset of the boundary. Closed problems arise, for example, in models of transonic fluid flow about a given profile, but very little is known on the well-posedness in spaces of weak solutions. We present recent progress, obtained in collaboration with D. Lupo and C.S. Morawetz, on the well-posedness in weighted Sobolev spaces as well as the beginnings of a regularity theory
Weak well-posedness of the Dirichlet problem for equations of mixed elliptic-hyperbolic type / K.R. Payne. - In: LE MATEMATICHE. - ISSN 0373-3505. - 60:2(2006), pp. 315-327.
Weak well-posedness of the Dirichlet problem for equations of mixed elliptic-hyperbolic type
K.R. PaynePrimo
2006
Abstract
Equations of mixed elliptic-hyperbolic type with a homogeneous Dirichlet condition imposed on the entire boundary will be discussed. Such colosed problems are typically overdetermined in spaces of classical solutions in contrast to the well-posedness for classical solutions that can result from opening the boundary by prescribing the boundary condition only on a proper subset of the boundary. Closed problems arise, for example, in models of transonic fluid flow about a given profile, but very little is known on the well-posedness in spaces of weak solutions. We present recent progress, obtained in collaboration with D. Lupo and C.S. Morawetz, on the well-posedness in weighted Sobolev spaces as well as the beginnings of a regularity theoryPubblicazioni consigliate
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