Harmonic functions in a cylinder which vanish on the boundary

Cylindrical Carleman's formula of subharmonic functions and its application

“…The set Ω × R = {P = (X, y) ∈ R n ; X ∈ Ω, y ∈ R} in R n is simply denoted by T n (Ω). We call it a cylinder (see [5][6][7]12]). In the following, we denote the sets Ω × I and ∂Ω × I with an interval I on R by T n (Ω; I) and S n (Ω; I) respectively.…”

Existence and boundary behavior of weak solutions for Schrödingerean TOPSIS equations

“…We can also refer the reader to Miyamoto (see [3]), Chen (see [5] and the references therein). Let α > 0 and 1 ≤ p < ∞.…”

“…In the Schrödingerean expectation framework, the notion of the corresponding Schrödingerean stochastic calculus of Itô type were also established (see [2]). As in [3], the set × R = P = (X, y) ∈ R n ; X ∈ , y ∈ R in R n is simply denoted by C n ( ). We call it a cylinder (see [3]).…”

“…As in [3], the set × R = P = (X, y) ∈ R n ; X ∈ , y ∈ R in R n is simply denoted by C n ( ). We call it a cylinder (see [3]). On that basis, the theory and applications of the Schrödingerean TOPSIS equation have been developed rapidly (see [2,[4][5][6][7][8][9][10][11] and the references therein).…”

“…ℵ p 0 ( ) is studied in [5] and [3,6] on the setting of upper half-space and bounded smooth domain in R n , respectively.…”