L^{p}-regularity results for 2m-th order parabolic equations in time-varying domains
Arezkı Kheloufı, Abderrahmane Ikassoulene · Miskolc mathematical notes/Mathematical notes · 2022
This paper is devoted to the analysis of the following linear 2m-th order parabolic equation ∂ t u+(-1) m ∑ N k=1 ∂ 2mx k u = f , subject to Dirichlet type condition ∂ l ν u = 0, l = 0, 1, ..., m-1, on the lateral boundary, where m is a positive integer.The right-hand side f of the equation is taken in the Lebesgue space L p , 1 < p < +∞.The problem is set in a domain of the form2010