Quantitative continuation from a measurable set of solutions of elliptic equations
Copyright policy )Quantitative continuation from a measurable set of solutions of elliptic equations
Consider an open bounded connected set Ω in Rn and a Lebesgue measurable set E ⊂⊂ Ω of positive measure. Let u be a solution of the strictly elliptic equation Di (aij Dj u) = 0 in Ω, where aij ∈ C0, 1 (Ω̄) and {aij} is a symmetric matrix. Assume that |u| ≤ ε in E. We quantify the propagation of smallness of u in Ω.
propagation of smallness, doubling theorem, Variational methods for second-order elliptic equations, PDEs with low regular coefficients and/or low regular data, quantitative continuation, three-balls theorems, Stability in context of PDEs, Continuation and prolongation of solutions to PDEs
propagation of smallness, doubling theorem, Variational methods for second-order elliptic equations, PDEs with low regular coefficients and/or low regular data, quantitative continuation, three-balls theorems, Stability in context of PDEs, Continuation and prolongation of solutions to PDEs
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