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Open AccessMonotone iterations of two obstacle problems with different operators
In this paper we analyze iterations of the obstacle problem for two different operators. We solve iteratively the obstacle problem from above or below for two different differential operators with obstacles gi...
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Homogenization for Nonlocal Evolution Problems with Three Different Smooth Kernels
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Asymptotic \(C^{1,\gamma }\) -regularity for value functions to uniformly elliptic dynamic programming principles
In this paper we prove an asymptotic \(C^{1,\gamma }\) C ...
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A game theoretical approximation for solutions to nonlinear systems with obstacle-type equations
In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is an obstacle type equation, $$\min \{...
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Mixing Local and Nonlocal Evolution Equations
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We introduce a notion of fractional convexity that extends naturally the usual notion of convexity in the Euclidean space to a fractional setting. With this notion of fractional convexity, we study the fractio...
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A convection–diffusion model on a star-shaped graph
In this paper we study a convection–diffusion equation on a star-shaped graph composed by n incoming edges and m outgoing edges with a nonlinearity ...
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The First Eigenvalue for Nonlocal Operators
In this chapter we present some results concerning the first eigenvalue for a nonlocal operator in convolution form with a smooth kernel. Given a bounded domain
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Splitting methods and numerical approximations for a coupled local/nonlocal diffusion model
In this paper, we study a splitting approach and a numerical method to approximate solutions to an evolution problem that couples local and nonlocal diffusion operators. The method proposed here takes advantag...
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Asymptotic behaviour for local and nonlocal evolution equations on metric graphs with some edges of infinite length
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An Asymptotic Mean Value Formula for Eigenvalues of the Hessian Related to Concave/Convex Envelopes
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Nonlocal perimeter, curvature and minimal surfaces for measurable sets
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Let \(\Omega \subset {\mathbb {R}}^{n}\) Ω ...
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An Obstacle Problem for Nonlocal Equations in Perforated Domains
In this paper we analyze the behavior of solutions to a nonlocal equation of the form J ∗ u (x) − u (x) = f (x) in a perforated domain Ω ∖ A 𝜖 with u = 0 in ...
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A concave–convex problem with a variable operator
We study the following elliptic problem \(-A(u) = \lambda u^q\) ...
