Affiliations: Institute of Mathematics, The Hebrew University, Givat Ram, Jerusalem, Israel
Note: [] Correspondence to: A. Eizenberg, Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel.
Note: [] Sponsored in part by the Landau Center for Mathematical Research in analysis, supported by the Minerva Foundation (Federal Republic of Germany).
Note: [] Supported in Part by the US-Israel BSF.
Abstract: A Hamilton–Jacobi equation, with a convex Hamiltonian such that the corresponding Langrangean vanishes along the orbits of certain dynamical systems, is considered. Small elliptic and inhomogeneous perturbations of such HJE are studied in bounded domains. In the problem at hand the HJE may have more than one viscosity solution under zero boundary conditions, which brings up the question of uniqueness conditions. It is found that under the uniqueness conditions the problem can be reduced to the linear case by a completely new method (notice that the logarithmic transformation, generally speaking, cannot be applied in the considered problem).
