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Results tagged with ap.analysis-of-pdes
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user 102183
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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votes
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answer
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Quantitative lower bound for the Modica Mortola Inequality
Suppose $\Omega\subset\mathbb{R}^n$ is an open, bounded Lipschitz domain. Consider the sequences of energies
$$E_\varepsilon (u) := \int_\Omega \varepsilon |\nabla u|^2 + \frac{1}{\varepsilon} (1 - …
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