Estimate for gradient, bmo and Lindelöf theorem
Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.
Estimates for the Poisson kernel on higher rank NA groups
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
Estimates for the Poisson kernels and their derivatives on rank one NA groups
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.
Estimates of Green functions and their applications for parabolic operators with singular potentials
We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.
Estimates of -harmonic conjugate operator.
Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition.
Exact solutions to some external mixed problems in potential theory
A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several...
Existence and geometric properties of solutions of a free boundary problem in potential theory.
Existence and regularity for a minimum problem with free boundary.
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem.
Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.
Existence of solutions for a family of polyharmonic and biharmonic equations.
Extensions of operators and the Dirichlet problem in potential theory
Extremal length of vector measures.
Extremal plurisubharmonic functions and invariant pseudodistances
Extremal plurisubharmonic functions in