Mixed problems for pluriparabolic equations
The author considers linear partial differential operators with smooth coefficients in \({\mathbb{R}}_ t\times {\mathbb{R}}^ n_ x\), of the type \(P=\sum c_{k\lambda}(t,x)D^ k_ tD^{\lambda}_ x\) where \(k,\lambda =(\lambda_ 1,...,\lambda_ n)\) in the sum run over the set \(\{k+\sum^{n}_{j-1}\lambda_ j/p_ j\leq m\}\), for \(p_ 1,...,p_ n\) given with \(p_ 1=...=p_ s=1\), \(p_ j>1\) for \(j=s+1,...,n\) (one assumes \(s\geq 1).\) Under suitable assumptions of the symbol of P, a priori estimates are proved for the solutions of mixed problems, with Cauchy data at \(t=0\) and boundary conditions at \(x_ 1=0\).
scientific article; zbMATH DE number 4030113
scientific article