XXXIX Workshop on Geometric Methods in Physics 19.06–25.06.2022
XI School on Geometry and Physics 27.06–1.07.2022

Tomasz Żynda


Reproducing kernels and minimal solutions of elliptic equations


Suppose that the set of square-integrable solutions of an elliptic equation which take value equal to c in some given point is non-empty. Then there is exactly one element with minimal L^2 norm. Moreover such an element depends in continuous way on a weight of integration and on a domain of integration. These theorems can be proved by using the theory of reproducing kernels.







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University of Bialystok






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