If g is a nondecreasing nonnegative continuous function we prove that any solution of - Δu + g (u) = 0 in a half plane which blows-up locally on the boundary, in a fairly general way, depends only on the normal variable. We extend this result to problems in the complement of a disk. Our main application concerns the exponential nonlinearity g(u) = eau, or power-like growths of g at infinity. Our method is based upon a combination of the Kelvin transform and moving plane method.
Porretta, A., Veron, L. (2004). Symmetry properties of solutions of semilinear elliptic equations in the plane. MANUSCRIPTA MATHEMATICA, 115(2), 239-258 [10.1007/s00229-004-0498-1].
Symmetry properties of solutions of semilinear elliptic equations in the plane
PORRETTA, ALESSIO;
2004-01-01
Abstract
If g is a nondecreasing nonnegative continuous function we prove that any solution of - Δu + g (u) = 0 in a half plane which blows-up locally on the boundary, in a fairly general way, depends only on the normal variable. We extend this result to problems in the complement of a disk. Our main application concerns the exponential nonlinearity g(u) = eau, or power-like growths of g at infinity. Our method is based upon a combination of the Kelvin transform and moving plane method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
