Isolated singularities in fluid flow and elasticity

Foundations of potential theory

The purpose of this paper is to establish pointwise estimates for solutions of elliptic partial differential equations and systems. The results presented here differ from the familiar ones in that they give information about the behavior of solutions at individual points. More specifically, we obtain two kinds of results. On the one hand, we establish inequalities for solutions and their derivatives at isolated individual points. On the other, we also obtain results of the „almost everywhere“ type. Theorems 1 and 2 below summarize the main results.

Local properties of solutions of elliptic partial differential equations

On exterior boundary value problems in linear elasticity

Handbuch der Physik - Encyclopedia of Physics. Herausgegeben von S. Flügge. Band 17: Dielektrika. VI, 406 Seiten mit 198 Figuren. Gr.-8°. Springer-Verlag, Berlin-Göttingen-Heidelberg 1956. Preis: Ganzleinen DM 94,—

We shall operate in N-dimensional euclidean space EN, N _ 2, and use the following notation. x = (xI, *.* , XN) and B(x, r) = the open N-ball with center x and radius r. Also, we shall adopt the convention that if P(x) is a polynomial of degree less than zero, then P(x) is identically zero. We say the function f(x) is in T'(x,), a c N, if f(x) is in L' in a neighborhood of the point x0, and if there is a polynomial P(x) of degree strictly less than a such that

Isolated singularities in fluid flow and elasticity

References

Foundations of potential theory

Local properties of solutions of elliptic partial differential equations

On exterior boundary value problems in linear elasticity

Handbuch der Physik - Encyclopedia of Physics. Herausgegeben von S. Flügge. Band 17: Dielektrika. VI, 406 Seiten mit 198 Figuren. Gr.-8°. Springer-Verlag, Berlin-Göttingen-Heidelberg 1956. Preis: Ganzleinen DM 94,—

Removable Sets for Pointwise Solutions of the Generalized Cauchy-Riemann Equations

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