Titlebook: Beyond Sobolev and Besov; Regularity of Soluti Cornelia Schneider Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusiv

行業(yè)

Symbols and terms used in Parts 1–4tudy all relevant function spaces needed later on, which are of interest for their own sake. The material is presented according to our needs. In some parts we merely collect what is needed avoiding detailed proofs but providing references for further reading. At other places we develop the existing

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M. W. Tate,E. F. Eikenberry,S. M. Grunerthe notions of elliptic, parabolic, and hyperbolic PDEs, since we are going to study the regularity of solutions for all these types of equations in Chaps. .–.. In the subsequent sections we study weak formulations of our PDEs. In a weak formulation an equation is no longer required to hold absolute

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S. M. Gruner,E. F. Eikenberry,M. W. Tatel equations. The nonlinear term .(., .) we consider in this context is quite general and required to satisfy a growth condition w.r.t. its partial derivatives. In our considerations we pay special attention to monomials, i.e., when . is of the form .(., .)?=?.., where . with .?≥?2, and give precise

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Royalty and Fees for Technical Services,es defined on noncompact Riemannian manifolds .. Here . is of dimension . and . of dimension . with .?

Painstaking

Cornelia SchneiderGives a comprehensive treatment of the relations between complex function spaces, the regularity theory of PDEs and traces.Includes many figures illustrating connections and basic ideas.Provides a sys

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Reverie

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Symbols and terms used in Parts 1–4The principal object of this manuscript is to study on the one hand the regularity of solutions of . in specific scales of function spaces and traces of such functions on the boundary of domains and submanifolds on the other hand.

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Principles of monochromatic data collectionThe present chapter is the heart of Part I of this manuscript dealing with the regularity theory of PDEs. In contrast to Chap. . we now consider parabolic problems and the (spacial) fractional Sobolev and Besov regularity of their solutions.

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https://doi.org/10.1107/97809553602060000106In this chapter we study linear hyperbolic equations (6.1.1) of second order on special Lipschitz domains according to Definition .. For these kinds of equations regularity estimates in Kondratiev spaces were derived in which enable us to treat these equations in a similar way as the parabolic problems in Chap. ..