On the regularity of the heat equation solution in non-cylindrical domains: Two approaches

On Parabolic Equations with Mixed Dirichlet–Robin Type Boundary Conditions in a Non-rectangular Domain

“…We can work directly in the non-regular domains and we obtain singular solutions (see, for example [4]), or we impose conditions on the non-regular domains to obtain regular solutions (see, for example [8] and [5]). It is the second approach that we follow in this work.…”

On a Second Order Linear Parabolic Equation with Variable Coefficients in a Non-Regular Domain of R³

“…It is well known that there are two main approaches for the study of boundary value problems in such non-smooth domains. We can work directly in the non-regular domains and we obtain singular solutions (see, for example [3,16,18] and [20]), or we impose conditions on the non-regular domains (and on the coefficients) to obtain regular solutions (see, for example [2,17] and [30]). It is the second approach that we follow in this work.…”

Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1

“…In Sadallah [18], the same problem has been studied for a 2 -parabolic operator in the case of one space variable. Further references on the analysis of parabolic problems in non-cylindrical domains are: Savaré [19], Aref'ev and Bagirov [3], Ho mann and Lewis [8], Labbas, Medeghri and Sadallah [13,14], Alkhutov [1,2] and Khelou et al [9][10][11][12]. There are many other works concerning boundary-value problems in non-smooth domains (see, for example, Grisvard [7] and the references therein).…”