Some monotonicity results for minimizers in the calculus of variations
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Publication:387248
DOI10.1016/j.jfa.2013.02.005zbMath1278.49029arXiv1209.1517OpenAlexW2963477643MaRDI QIDQ387248
Enrico Valdinoci, Ovidiu V. Savin
Publication date: 20 December 2013
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1209.1517
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Cites Work
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- Regularity of nonlocal minimal cones in dimension 2
- \(C^{2,\alpha}\) regularity of flat free boundaries for the thin one-phase problem
- Energy estimates and 1-D symmetry for nonlinear equations involving the half-Laplacian
- On a conjecture of De Giorgi and some related problems
- Elliptic partial differential equations of second order
- New Liouville theorems for linear second order degenerate elliptic equations in divergence form.
- Regularity of flat level sets in phase transitions
- Regularity properties of nonlocal minimal surfaces via limiting arguments
- Bernstein and De Giorgi type problems: new results via a geometric approach
- Nonlocal minimal surfaces
- Variational problems with two phases and their free boundaries
- Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
- Global energy minimizers for free boundary problems and full regularity in three dimensions
- Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
- An Extension Problem Related to the Fractional Laplacian
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- Layer solutions in a half‐space for boundary reactions
- On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
