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Award ID contains: 1854788

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  1. (, Bollettino dell'Unione Matematica Italiana)
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  2. (, Journal of the European Mathematical Society)
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  3. (, The Journal of Geometric Analysis)
    null (Ed.)
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  4. (, Proceedings of the American Mathematical Society)
    null (Ed.)
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  5. ; (, Discrete & Continuous Dynamical Systems)
    We give a proof by foliation that the cones over \begin{document}$$ \mathbb{S}^k \times \mathbb{S}^l $$\end{document} minimize parametric elliptic functionals for each \begin{document}$$ k, \, l \geq 1 $$\end{document}. We also analyze the behavior at infinity of the leaves in the foliations. This analysis motivates conjectures related to the existence and growth rates of nonlinear entire solutions to equations of minimal surface type that arise in the study of such functionals. 
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  6. (, International Mathematics Research Notices)
    Abstract We construct examples of complex-valued singular solutions to linear, uniformly parabolic equations with complex coefficients in dimension $$n \geq 2$$, which are exactly as irregular as parabolic energy estimates allow. 
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  7. (, Calculus of Variations and Partial Differential Equations)
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  8. ; (, Analysis & PDE)
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