DOI: 10.1007/978-3-319-00125-8_2
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Abstract: In this paper we consider the non-uniqueness and the uniqueness property for the solutions to the Cauchy problem for the operators Eu=∂2tu+∑k,l=1n∂xk(akl(t,x)∂xlu)+β(t,x)∂tu+∑m=1nbm(t,x)∂xmu+c(t,x)u and Pu=∂tu+∑k,l=1n∂xk(akl(t,x)∂xlu)+∑m=1nbm(t,x)∂xmu+c(t,x)u, where ∑nk,l=1akl(t,x)ξkξl|ξ|−2≥a0>0 . We study non-uniqueness and uniqueness in dependence of global and local regularity properties of the coefficients of the principal part. The global regularity will be ruled by the modulus of continuity of a kl on [0…

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