×

Approximation of generalized bi-axially symmetric potentials with fast rates of growth. (English) Zbl 0856.35005

Summary: The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials (GBSP’s). The GBSP’s are taken to be regular in a finite hyperball. The influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The authors obtain the characterizations of the \(q\)-type and lower \(q\)-type of a GBSP \(H\in H_R\), \(0< R< \infty\), in terms of the rate of decay of the approximation error \(E_n(H, R_0)\), \(0< R_0< R< \infty\).

MSC:

35A35 Theoretical approximation in context of PDEs
35J15 Second-order elliptic equations
35B40 Asymptotic behavior of solutions to PDEs
PDFBibTeX XMLCite