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Nodal sets for solutions of elliptic equations. (English) Zbl 0692.35005
There is studied the nodal set of an elliptic equation with bounded coefficients, those of the elliptic part being continuous. The principal result is that the Hausdorff measure of the nodal set is finite in a neighborhood of any point at which the solution vanishes of finite order. First, an estimate is given for the nodal set of polynomials and harmonic polynomials, using some inequalities given by H. Federer [Geometric measure theory (1969; Zbl 0177.008)]. Application are given to the nodal set of eigenfunctions of the Laplacian operator on a compact Riemannian manifold.
Reviewer: G.Pasa

MSC:
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35Jxx Elliptic equations and elliptic systems
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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