A construction of parametrices of elliptic boundary value problems. (English) Zbl 0826.35032

Bergamasco, Adalberto P.; Petronilho, Gerson

Port. Math. 50, No. 3, 263-276 (1993).

The authors study the regularity for problems \[ Pu = f \text{ in } \Omega \subset \mathbb{R}^{n + 1}, \quad D^p_y u = g_p,\;p = \overline {0,m - 1} \text{ in } \partial \Omega, \tag{1} \] where \(\Omega\) is smooth and the operator \(P\) is of order \(2m\), linear with smooth coefficients and properly elliptic. There are \(m\) boundary conditions and the Lopatinskij-Shapiro conditions are assumed to be verified. A new way of obtaining approximate solutions of problem (1) is presented. Solutions are expressed by means of parametrices.

Reviewer: R.Kodnár (Bratislava)

MSC:

35J40	Boundary value problems for higher-order elliptic equations
35D10	Regularity of generalized solutions of PDE (MSC2000)
35S15	Boundary value problems for PDEs with pseudodifferential operators

Keywords:

Lopatinskij-Shapiro conditions; approximate solutions