Weak maximum principle for elliptic operators on a stratified set

yesIn this paper, we discuss the weak maximum principle for an elliptic equation on an arbitrary stratified set. Early, we have succeeded in doing this only on a two-dimensional stratified setVoronezh State Universit

The mean-value theorem for elliptic operators on stratified sets

yesIn this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principleBelgorod State Universit

Maximum principle for subharmonic functions on a stratified set

yesThe strong maximum principle is proved for solutions of the inequality ∆u≥0 on a stratified setBelgorod State Universit

The mean-value theorem for elliptic operators on stratified sets

In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principleyesBelgorod State Universit

Maximum principle for subharmonic functions on a stratified set

The strong maximum principle is proved for solutions of the inequality ∆u≥0 on a stratified setyesBelgorod State Universit

A necessary condition for an extremum on a stratified set

yesIn this paper, on a connected set composed of finitely many convex polyhedra of different dimensions, we introduce a special (stratified) measure and define a divergence operator (as the flow density of the tangent vector field) and a Laplacian on smooth functionsBelgorod State Universit

Weak maximum principle for elliptic operators on a stratified set

In this paper, we discuss the weak maximum principle for an elliptic equation on an arbitrary stratified set. Early, we have succeeded in doing this only on a two-dimensional stratified setyesVoronezh State Universit