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Creators/Authors contains: "Otárola, Enrique"

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  1. ; ; (, Journal of Differential Equations)
    We prove the well posedness in weighted Sobolev spaces of certain linear and nonlinear elliptic boundary value problems posed on convex domains and under singular forcing. It is assumed that the weights belong to the Muckenhoupt class with ). We also propose and analyze a convergent finite element discretization for the nonlinear elliptic boundary value problems mentioned above. As an instrumental result, we prove that the discretization of certain linear problems are well posed in weighted spaces. 
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    Free, publicly-accessible full text available December 1, 2025
  2. ; (, Numerische Mathematik)
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  3. ; ; (, Mathematical Models and Methods in Applied Sciences)
    null (Ed.)
    In Lipschitz two- and three-dimensional domains, we study the existence for the so-called Boussinesq model of thermally driven convection under singular forcing. By singular we mean that the heat source is allowed to belong to [Formula: see text], where [Formula: see text] is a weight in the Muckenhoupt class [Formula: see text] that is regular near the boundary. We propose a finite element scheme and, under the assumption that the domain is convex and [Formula: see text], show its convergence. In the case that the thermal diffusion and viscosity are constants, we propose an a posteriori error estimator and show its reliability. We also explore efficiency estimates. 
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  4. ; ; (, Mathematics of Computation)
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  5. ; (, Applied Mathematics Letters)
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  6. ; ; (, SIAM Journal on Scientific Computing)
    null (Ed.)
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  7. ; (, Journal of Mathematical Analysis and Applications)
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  8. ; ; (, Computers & Mathematics with Applications)
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  9. ; ; (, Computer Methods in Applied Mechanics and Engineering)
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  10. ; (, Fractional Calculus and Applied Analysis)
    Abstract We consider an evolution equation involving the fractional powers, of order s ∈ (0, 1), of a symmetric and uniformly elliptic second order operator and Caputo fractional time derivative of order γ ∈ (1, 2]. Since it has been shown useful for the design of numerical techniques for related problems, we also consider a quasi–stationary elliptic problem that comes from the realization of the spatial fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi–infinite cylinder. We provide existence and uniqueness results together with energy estimates for both problems. In addition, we derive regularity estimates both in time and space; the time–regularity results show that the usual assumptions made in the numerical analysis literature are problematic. 
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