Mathematics of the USSR-Sbornik · 1971 · 27 citations · 3 references
Natural SciencesMechanical EngineeringDifferential EquationsFinite Element AnalysisFinite Element MethodsBoundary ConditionsBoundary-value ProblemsPartial Differential EquationsElliptic Boundary-value ProblemsExponential GrowthPoisson's Equation
It is known that if an analytic function on the disk has exponential growth approaching the boundary, then it has generalized boundary values with which by means of Poisson kernels one can regenerate the function. In this work it is proved that similar properties are also possessed by the generalized solutions of elliptic equations in a bounded region of n-dimensional space. The main results were announced earlier (see MR 41 #3968). Bibliography: 18 references.
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S. G. Kreĭn, Yu. I. Petunin · Russian Mathematical Surveys · 1966 · 188 citations
On $L^p$ Estimates and Regularity II.
Martin Schechter · MATHEMATICA SCANDINAVICA · 1963 · 58 citations · Full text