Geodesic
Fully nonlinear free transmission problems
Edgard A. Pimentel1 orcid ; Makson S. Santos2
1Universidade de Coimbra, Portugal
2Instituto Superior Técnico, Lisbon, Portugal
Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 325-342

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DOI

We examine a free transmission problem driven by fully nonlinear elliptic operators. Since the transmission interface is determined endogenously, our analysis regards this object as a free boundary. We start by relating our problem with a pair of viscosity inequalities. Then, approximation methods ensure that strong solutions are of class C1,Log-Lip, locally. In addition, under further conditions on the problem, we prove quadratic growth of the solutions away from branch points.
DOI : 10.4171/ifb/489
Classification : 35-XX
Mots-clés : free transmission problems, fully nonlinear operators, regularity of the solutions, quadratic growth at branch points

Edgard A. Pimentel  1   ; Makson S. Santos  2

1 Universidade de Coimbra, Portugal
2 Instituto Superior Técnico, Lisbon, Portugal 
Edgard A. Pimentel; Makson S. Santos. Fully nonlinear free transmission problems. Interfaces and free boundaries, Tome 25 (2023) no. 3, pp. 325-342. doi: 10.4171/ifb/489
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     title = {Fully nonlinear free transmission problems},
     journal = {Interfaces and free boundaries},
     pages = {325--342},
     year = {2023},
     volume = {25},
     number = {3},
     doi = {10.4171/ifb/489},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/489/}
}
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