21 citations · 42 across the 4 of their papers we have counts for
4 papers
On Second Order Elliptic and Parabolic Equations of Mixed Type
Gong Chen, Mikhail Safonov
It is known that solutions to second order uniformly elliptic and parabolic equations, either in divergence or nondivergence (general) form, are Hölder continuous and satisfy the i…
Boundary estimates for positive solutions to second order elliptic equations
Mikhail V. Safonov
Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary…
On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations
Hongjie Dong, Seick Kim, Mikhail Safonov
We study boundary blow-up solutions of semilinear elliptic equations with , or with , where is a second order elliptic operator with measurable…
Doubling properties for second order parabolic equations
Mikhail V. Safonov, Yu Yuan
We prove the doubling property of L-caloric measure corresponding to the second order parabolic equation in the whole space and in Lipschitz domains. For parabolic equations in the…