Boundary Unique Continuation on $$C^1$$-Dini Domains and the Size of the Singular Set
Sign Up to like & getrecommendations! Published in 2022 at "Archive for Rational Mechanics and Analysis"
DOI: 10.1007/s00205-022-01771-7
Abstract: Let $u$ be a harmonic function in a $C^1$-Dini domain $D$ such that $u$ vanishes on a boundary surface ball $\partial D \cap B_{5R}(0)$. We consider an effective version of its singular set (up to… read more here.
Keywords: set boundary; unique continuation; boundary unique; dini ... See more keywords
Convex functionals and the stratification of the singular set of their stationary points
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DOI: 10.1016/j.aim.2018.08.008
Abstract: We prove partial regularity of stationary solutions and minimizers $u$ from a set $\Omega\subset \mathbb R^n$ to a Riemannian manifold $N$, for the functional $\int_\Omega F(x,u,|\nabla u|^2) dx$. The integrand $F$ is convex and satisfies… read more here.
Keywords: stratification; convex functionals; singular set; set stationary ... See more keywords