Local properties of solutions of elliptic partial differential equations
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.
KeywordsCompact Support Taylor Expansion Differentiable Function Inverse Fourier Transform Singular Integral Operator
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