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Regular version of the site

Article

On uniqueness problems related to elliptic equations for measures

Journal of Mathematical Sciences. 2011. Vol. 176. No. 6. P. 759-773.

We consider elliptic equations for measures. Solutions are considered in the class of probability measures and in the class of signed measures with integrable densities. We discuss the following problems: When is a probability solution to this equation unique? When does a given probability solution have the property that any integrable solution is a multiple of it? Which dimension can have the simplex of probability solutions? We present some recent positive results, give counterexamples and formulate open problems.