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On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak
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Vladimir G. Maz'ya
Published/Copyright:
March 10, 2010
Abstract
We describe the dual space of the boundary trace space for functions with a finite Dirichlet integral for a domain with a vertex of an isolated cusp at the boundary. This leads to conditions of solvability of the Neumann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for 𝑞 such that the Neumann problem is solvable if the boundary function is in 𝐿𝑞 over the boundary of a domain with an outer peak.
Received: 2006-11-17
Published Online: 2010-03-10
Published in Print: 2007-September
© Heldermann Verlag
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Articles in the same Issue
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- On Doubly Periodic Solutions of Nonlinear Hyperbolic Equations of Higher Order
- Analytic Function Theory in Algebras
- Complex Geometry of the Universal Teichmüller Space. II
- On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak
- Stagnation Zones of 𝐴-Solutions
- On a Periodic Boundary Value Problem for Fourth Order Linear Functional Differential Equations
- On the Stability in Bonnet's Theorem of the Surface Theory
- On Some Properties of Solutions of Polyharmonic Equation in Polyhedral Angles
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