Separating variables in two‐way diffusion equations

Equations in Two Space Variables

Hölder estimates for spatial second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.

Linear equations in quaternionic variables

We study the quaternionic linear system which is composed out of terms of the form ln(x) := ∑n p=1 apxbp with quaternionic constants ap, bp and a variable number n of terms. In the first place we investigate one equation in one variable. If n = 2 the corresponding equation, which is normally called Sylvester’s equation will be treated completely by using only quaternionic algebra. For larger n ...

Similarity Variables and an Oleinik Type Estimate for Convection-diffusion Equations

Word Equations with Two Variables

The problem whether the set of all equations that are satisfiable in some free semigroup or, equivalently, in an algebra of words with concatenation is recursive (usually called the satisfiability problem for semigroup equations) was first formulated by A.A. Markov in early sixties (see [3]). Special cases of the problem were solved affirmatively by A.A. Markov (see [3]), Yu.I. Khmelevskiı̆ [8],...

Complex Variables and Elliptic Equations