| Abstract: |
| In this talk, we consider boundary energies generated by convex functions. Motivated by recent work by Buttazzo--Ognibene (arXiv:2506.06914) on nonlinear Robin energies with power-type boundary nonlinearities, we study asymptotics for nonlinear Robin energies with more general boundary nonlinearities. While the power case already reveals the Dirichlet and Neumann limiting behaviors, it is natural to ask whether the same mechanism remains valid beyond polynomial growth. Our aim is not only to enlarge the class of admissible nonlinearities, but also to replace arguments tied to explicit power computations with a unified variational framework based on convex duality and Moreau--Yosida regularization. This approach identifies the leading-order asymptotic term through the convex conjugate of the boundary energy and yields quantitative control of the remainder under suitable assumptions. In this way, we recover the classical power-type situation as a special case, while covering genuinely non-power boundary responses that lie outside the scope of explicit model-dependent calculations. These results provide a variational perspective on how Dirichlet- and Neumann-type limits emerge from nonlinear boundary penalization. |
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