The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains
Abstract
We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.
Keywords
boundary value problems; weak solutions; second order elliptic linear equations; unbounded domains; Dini-continuity
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Wydział Matematyki i Informatyki, Uniwersytet Warmińsko-Mazurski w Olsztynie Poland
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