Full text  
Author(s): 
Ebert, M. R.
;
Kapp, R. A.
;
Picon, T.
Total Authors: 3

Document type:  Journal article 
Source:  Annali di Matematica Pura ed Applicata; v. 195, n. 4, p. 10811091, AUG 2016. 
Web of Science Citations:  1 
Abstract  
It is well known that, for space dimension n > 3, one cannot generally expect L1Lp estimates for the solution of u(tt)  Delta u = 0, u(0, x) = 0, u(t) (0, x) = g(x), where (t, x) is an element of R+ x Rn. In this paper, we investigate the benefits in the range of 1 <= p <= q such that LpLq estimates hold under the assumption of radial initial data. In the particular case of odd space dimension, we prove L1Lq estimates for 1 <= q < 2n/n1 and apply these estimates to study the global existence of small data solutions to the semilinear wave equation with power nonlinearity vertical bar u vertical bar(sigma), sigma > sigma(c) (n), where the critical exponent sigma(c)(n) is the Strauss index. (AU)  
FAPESP's process:  13/176365  A priori estimates for elliptic complexes and applications 
Grantee:  Tiago Henrique Picon 
Support type:  Research Grants  Young Investigators Grants 
FAPESP's process:  13/202978  Decay estimates for hyperbolic partial differential equations in the L^pL^q framework 
Grantee:  Marcelo Rempel Ebert 
Support type:  Scholarships abroad  Research 