AbstractWe examine the asymptotic behaviors of solutions to Hamilton-Jacobi equations with state constraints while varying the underlying domains. We establish a connection between the convergence of these solutions and the regularity of the additive eigenvalues in relation to the domains. To accomplish this, we introduce a framework based on Mather measures that enables us to compute the one-s...
AbstractMany moduli spaces in geometry and physics, like those appearing in symplectic topology, quantum gauge field theory and in relation to homological mirror symmetry, are constructed as parametrizing spaces of solutions to nonlinear elliptic differential operators modulo symmetries of the underlying theory. A plethora of difficulties arise in constructing such spaces; for instance, the spa...
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