Poincaré–Lelong equation via the Hodge–Laplace heat equation

Poincaré-Lelong equation via the Hodge Laplace heat equation

In this paper, we develop new methods of solving the Poincaré-Lelong equation. It is mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is shown to be effective through obtaining better, sometimes optimal, existence results for the Poincaré-Lelong equation.

Heat Equation and Multipliers via the Wave Equation

Recently, Nagel and Stein studied the b-heat equation, where b is the Kohn Laplacian on the boundary of a weakly-pseudoconvex domain of finite type in C. They showed that the Schwartz kernel of e b satisfies good “off-diagonal” estimates, while that of e b −π satisfies good “on-diagonal” estimates, where π denotes the Szegö projection. We offer a simple proof of these results, which easily gene...

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

Discrete Scale Spaces via Heat Equation

Scale spaces allow us to organize, compare and analyse differently sized structures of an object. The linear scale space of a monochromatic image is the solution of the heat equation using that image as an initial condition. Alternatively, this linear scale space can also be obtained applying Gaussian filters of increasing variances to the original image. In this work, we compare (by looking at...

The Heat Equation