Half-space Gaussian symmetrization: applications to semilinear elliptic problems

We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 10; no. 1; pp. 1201 - 1221
Main Authors Díaz, J. I., Feo, F., Posteraro, M. R.
Format Journal Article
LanguageEnglish
Published De Gruyter 14.04.2021
Subjects
35B45
35J61
35J70
Gauss measure
Gaussian symmetrization
semilinear equations
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Summary:We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness of a solution in ℝ without growth restrictions at infinity. A comparison result in terms of the half-space Gaussian symmetrized problem is also proved. As an application, we give some estimates in measure of the growth of the solution near the boundary of its support for sublinear equations. Finally we generalize our results to problems with a nonlinear zero order term not necessary of power type.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2020-0169