Two-sided Gaussian bounds for fundamental solutions of non-divergence form parabolic operators with Hölder continuous coefficients


Abstract


We establish two-sided Gaussian bounds for fundamental solutions of general non-divergence form parabolic operators with Hölder continuous coefficients. The result we obtain is essentially based on parametrix method.

DOI Code: 10.1285/i15900932v40n2p21

Keywords: Non-divergence form parabolic operator; fundamental solution; parametrix; twosided Gaussian bounds; Dirichlet-Green function; Neumann-Green function

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