TY - JOUR
T1 - Hypoellipticity of certain degenerate elliptic boundary value problems
AU - Kannai, Yakar
PY - 1976
Y1 - 1976
N2 - The concept of hypoellipticity for degenerate elliptic boundary value problems is defined, and its relation with the hypoellipticity of certain pseudo-differential operators on the boundary is discussed (for second order equations). A theorem covering smoothness of solutions of boundary value problems such as a(x)∂u/∂n + b(x)u =f(x) for the Laplace equation is proved. An almost complete characterization of hypoelliptic boundary value problems for elliptic second order equations in two dimensions is given via analysis of hypoelliptic pseudo-differential operators in one variable.
AB - The concept of hypoellipticity for degenerate elliptic boundary value problems is defined, and its relation with the hypoellipticity of certain pseudo-differential operators on the boundary is discussed (for second order equations). A theorem covering smoothness of solutions of boundary value problems such as a(x)∂u/∂n + b(x)u =f(x) for the Laplace equation is proved. An almost complete characterization of hypoelliptic boundary value problems for elliptic second order equations in two dimensions is given via analysis of hypoelliptic pseudo-differential operators in one variable.
KW - Boundary value problems
KW - Elliptic equations
KW - Hypoelliptic pseudo-differential operators
KW - Ordinary pseudo-differential operators
KW - Symbols
UR - http://www.scopus.com/inward/record.url?scp=84968468872&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1976-0407436-4
DO - 10.1090/S0002-9947-1976-0407436-4
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AN - SCOPUS:84968468872
SN - 0002-9947
VL - 217
SP - 311
EP - 328
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
ER -