Regularizing Effect in Singular Semilinear Problems

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URI: https://hdl.handle.net/10481/85635
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Autor
Carmona Tapia, José; Martínez Aparicio, Antonio Jesús; Martínez Aparicio, Pedro J.; Martínez-Teruel, Miguel
Editorial
Vilnius Gediminas Technical University, Lithuania
Materia
Nonlinear elliptic equations
 
Singular problem
 
Regularizing effect
 
Fecha
2023
Referencia bibliográfica
Carmona, J., Martínez Aparicio, A. J., Martínez-Aparicio, P. J., & Martínez-Teruel, M. (2023). Regularizing effect in singular semilinear problems. Mathematical Modelling and Analysis, 28(4), 561–580. [https://doi.org/10.3846/mma.2023.18616]
Patrocinador
Ministerio de Ciencia, Innovación y Universidades, Agencia Estatal de Investigación PID2021-122122NB-I00 (FEDER); Junta de Andalucía; Unión Europea P18-FR-667; Junta de Andalucía FQM-194, FQM-116, UAL2020-FQM-B2046; CDTIME; Ministerio de Universidades FPU21/04849, FPU21/05578
Resumen
We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is-triangle u+ g(x, u) = f (x)/u(gamma) in Omega, u = 0 on partial derivative Omega, where Omega is a bounded open set of R-N, gamma > 0, f (x) is a nonnegative function in L-1(Omega) and g(x, s) is a Caratheodory function. In a framework where no H-0(1) (Omega) solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.
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