We study the regularizing effect arising from the interaction between the coefficient a of the zero-order term and the datum f in the problem (Formula presented.) where Ω⊆RN is a bounded domain and L is an X-elliptic operator introduced by Lanconelli and Kogoj (X-elliptic operators and X-control distances, pp 223–243, 2000). If f∈L1(Ω), we prove that the Q-condition introduced by Arcoya and Boccardo (J Funct Anal 268(5):1153–1166, 2015) is sufficient to ensure the existence and boundedness of solutions in the framework of X-elliptic operators as well. Finally, we prove the existence of a bounded solution for linear problems under a more general condition between f and a.
Regularizing effect of the interplay between coefficients in linear and semilinear X-elliptic equations
Molica Bisci, Giovanni;
2026-01-01
Abstract
We study the regularizing effect arising from the interaction between the coefficient a of the zero-order term and the datum f in the problem (Formula presented.) where Ω⊆RN is a bounded domain and L is an X-elliptic operator introduced by Lanconelli and Kogoj (X-elliptic operators and X-control distances, pp 223–243, 2000). If f∈L1(Ω), we prove that the Q-condition introduced by Arcoya and Boccardo (J Funct Anal 268(5):1153–1166, 2015) is sufficient to ensure the existence and boundedness of solutions in the framework of X-elliptic operators as well. Finally, we prove the existence of a bounded solution for linear problems under a more general condition between f and a.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
