Celebratio Mathematica — Morawetz

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D. Lupo, C. S. Morawetz, and K. R. Payne: “On closed boundary value problems for equations of mixed elliptic-hyperbolic type,” Comm. Pure Appl. Math. 60 : 9 (2007), pp. 1319–1348. An erratum to this article was published in Comm. Pure Appl. Math. 61:4 (2008). MR 2337506 Zbl 1125.35066 article

For partial differential equations of mixed elliptic-hyperbolic type we prove results on existence and existence with uniqueness of weak solutions for closed boundary value problems of Dirichlet and mixed Dirichlet-conormal types. Such problems are of interest for applications to transonic flow and are overdetermined for solutions with classical regularity. The method employed consists in variants of the \( a - b - c \) integral method of Friedrichs in Sobolev spaces with suitable weights. Particular attention is paid to the problem of attaining results with a minimum of restrictions on the boundary geometry and the form of the type change function. In addition, interior regularity results are also given in the important special case of the Tricomi equation.

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D. Lupo, C. S. Morawetz, and K. R. Payne: “Erratum: ‘On closed boundary value problems for equations of mixed elliptic-hyperbolic type’,” Comm. Pure Appl. Math. 61 : 4 (2008), pp. 594. Erratum to an article published in Comm. Pure Appl. Math. 60:9 (2007). MR 2383934 Zbl 1144.35451 article

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