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.
Malanchini, P., Molica Bisci, G., Secchi, S. (2026). Regularizing effect of the interplay between coefficients in linear and semilinear X-elliptic equations. JOURNAL OF EVOLUTION EQUATIONS, 26(2) [10.1007/s00028-025-01181-8].
Regularizing effect of the interplay between coefficients in linear and semilinear X-elliptic equations
Malanchini P.;Secchi S.
2026
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.
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