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Patrick van MeursStefania Patrizi. (2024) Discrete Dislocation Dynamics with Annihilation as the Limit of the Peierls–Nabarro Model in One Dimension. SIAM Journal on Mathematical Analysis 56:1, pages 197-233.
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Kui Li, Meng Yu & Zhitao Zhang. (2023) Liouville-type theorems for fractional Hardy–Hénon systems. Nonlinear Differential Equations and Applications NoDEA 31:1.
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Stefania Patrizi & Tharathep Sangsawang. (2023) Derivation of the 1-D Groma–Balogh equations from the Peierls–Nabarro model. Calculus of Variations and Partial Differential Equations 62:9.
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Annamaria Canino, Luigi Montoro, Berardino Sciunzi & Alessandro Trombetta. (2023) Variational properties of nonlocal singular problems. Nonlinearity 36:8, pages 4034-4052.
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Yuan Gao & Jean-Michel Roquejoffre. (2023) Asymptotic Stability for Diffusion with Dynamic Boundary Reaction from Ginzburg–Landau Energy. SIAM Journal on Mathematical Analysis 55:2, pages 1246-1263.
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Serena Dipierro, Stefania Patrizi & Enrico Valdinoci. 2023. Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs. Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs
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João Vitor da Silva, Pablo Ochoa & Analía Silva. (2021) Fractional elliptic problems with nonlinear gradient sources and measures. Revista Matemática Complutense 35:2, pages 485-514.
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Boumediene Abdellaoui, Ireneo Peral, Ana Primo & Fernando Soria. (2022) On the KPZ equation with fractional diffusion: Global regularity and existence results. Journal of Differential Equations 312, pages 65-147.
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Anup Biswas & Mitesh Modasiya. (2022) A study of nonlocal spatially heterogeneous logistic equation with harvesting. Nonlinear Analysis 214, pages 112599.
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María Laura de Borbón & Pablo Ochoa. (2020) A Capacity-Based Condition for Existence of Solutions to Fractional Elliptic Equations with First-Order Terms and Measures. Potential Analysis 55:4, pages 677-698.
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Franz Achleitner, Christian Kuehn, Jens M. Melenk & Alexander Rieder. (2021) Metastable speeds in the fractional Allen–Cahn equation. Applied Mathematics and Computation 408, pages 126329.
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Ahmed Youssfi & Ghoulam Ould Mohamed Mahmoud. (2021) Nonlocal semilinear elliptic problems with singular nonlinearity. Calculus of Variations and Partial Differential Equations 60:4.
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Yuan Gao, Jian-Guo Liu, Tao Luo & Yang Xiang. (2021) Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space. Discrete & Continuous Dynamical Systems - B 26:6, pages 3177.
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Stefania Patrizi & Tharathep Sangsawang. (2021) From the Peierls–Nabarro model to the equation of motion of the dislocation continuum. Nonlinear Analysis 202, pages 112096.
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Boumediene Abdellaoui & Antonio J. Fernández. (2020) Nonlinear fractional Laplacian problems with nonlocal ‘gradient terms’. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150:5, pages 2682-2718.
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Matteo Cozzi, Juan Dávila & Manuel del Pino. (2020) Long-time asymptotics for evolutionary crystal dislocation models. Advances in Mathematics 371, pages 107242.
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Ahmed Youssfi & Ghoulam Ould Mohamed Mahmoud. (2020) On Singular Equations Involving Fractional Laplacian. Acta Mathematica Scientia 40:5, pages 1289-1315.
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B. Barrios & A. Quaas. (2020) The sharp exponent in the study of the nonlocal Hénon equation in $${\mathbb {R}}^{N}$$: a Liouville theorem and an existence result. Calculus of Variations and Partial Differential Equations 59:4.
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Alessio Marinelli & Dimitri Mugnai. (2020) Fractional Generalized Logistic Equations with Indefinite Weight: Quantitative and Geometric Properties. The Journal of Geometric Analysis 30:2, pages 1985-2009.
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Claudianor O. Alves, Vincenzo Ambrosio & César E. Torres Ledesma. (2019) Existence of heteroclinic solutions for a class of problems involving the fractional Laplacian. Analysis and Applications 17:03, pages 425-451.
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Begoña Barrios & Maria Medina. (2019) Strong maximum principles for fractional elliptic and parabolic problems with mixed boundary conditions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, pages 1-21.
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Begoña Barrios, Luigi Montoro & Berardino Sciunzi. (2018) On the moving plane method for nonlocal problems in bounded domains. Journal d'Analyse Mathématique 135:1, pages 37-57.
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Serena Dipierro & Enrico Valdinoci. (2017) Continuity and density results for a one-phase nonlocal free boundary problem. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 34:6, pages 1387-1428.
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Stefania Patrizi & Enrico Valdinoci. (2017) Long-time behavior for crystal dislocation dynamics. Mathematical Models and Methods in Applied Sciences 27:12, pages 2185-2228.
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Serena Dipierro, Aram Karakhanyan & Enrico Valdinoci. (2017) A class of unstable free boundary problems. Analysis & PDE 10:6, pages 1317-1359.
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Serena Dipierro, María Medina, Ireneo Peral & Enrico Valdinoci. (2016) Bifurcation results for a fractional elliptic equation with critical exponent in
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B. Barrios, L. Del Pezzo, J. García-Melián & A. Quaas. (2017) Monotonicity of solutions for some nonlocal elliptic problems in half-spaces. Calculus of Variations and Partial Differential Equations 56:2.
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Matteo Cozzi & Enrico Valdinoci. (2017) Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium. Journal de l’École polytechnique — Mathématiques 4, pages 337-388.
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Serena Dipierro, Stefania Patrizi & Enrico Valdinoci. (2016) Chaotic Orbits for Systems of Nonlocal Equations. Communications in Mathematical Physics 349:2, pages 583-626.
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Stefania Patrizi & Enrico Valdinoci. (2016) Relaxation times for atom dislocations in crystals. Calculus of Variations and Partial Differential Equations 55:3.
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Claudia Bucur & Enrico ValdinociClaudia Bucur & Enrico Valdinoci. 2016. Nonlocal Diffusion and Applications. Nonlocal Diffusion and Applications
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Juan D?vila, Manuel del Pino, Serena Dipierro & Enrico Valdinoci. (2015) Concentration phenomena for the nonlocal Schr?dinger equation with Dirichlet datum. Analysis & PDE 8:5, pages 1165-1235.
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Stefania Patrizi & Enrico Valdinoci. (2014) Crystal Dislocations with Different Orientations and Collisions. Archive for Rational Mechanics and Analysis 217:1, pages 231-261.
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Stefania Patrizi & Enrico Valdinoci. (2015) Homogenization and Orowan?s law for anisotropic fractional operators of any order. Nonlinear Analysis: Theory, Methods & Applications 119, pages 3-36.
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Serena Dipierro & Enrico Valdinoci. (2015) On a fractional harmonic replacement. Discrete and Continuous Dynamical Systems 35:8, pages 3377-3392.
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