Integral and probabilistic representations for systems of elliptic equations |
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Affiliation: | Lavrentjev str., 6, Computing Center Russian Academy of Science, 630090 Novosibirsk, Russia |
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Abstract: | We present probabilistic representations for some systems of elliptic equations constructed as expectations of functionals of some specific Markov chains, in particular, the walk on spheres processes. These representations are deduced from converse mean value theorems that we prove for the equations under analysis, especially the Lamé equation of elasticity theory. We construct Monte Carlo algorithms, and estimate the variances and the cost. |
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