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The \(L^p\)-approximation of generalized bi-axially symmetric potentials. (English) Zbl 1216.35015

Summary: In this paper we deal 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). We obtain the characterization of \(q\)-type and lower \(q\)-type of a GBSP having fast rates of growth in terms of ratio of approximation errors in \(L^ p\) norm.

MSC:

35J15 Second-order elliptic equations
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
41A25 Rate of convergence, degree of approximation
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