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Semilinear elliptic equations with singular nonlinearities
Calculus of Variations and Partial Differential Equations, 2009We prove existence, regularity and nonexistence results for problems whose model is $$-\Delta u = \frac{f(x)}{u^{\gamma}}\quad {{\rm in}\,\Omega},$$ with zero Dirichlet conditions on the boundary of an open, bounded subset Ω of \({\mathbb{R}^{N}}\). Here γ > 0 and f is a nonnegative function on Ω.
BOCCARDO, Lucio, ORSINA, Luigi
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G-convergence and semilinear elliptic equations
Asymptotic Analysis, 1991We study the behavior of positive solutions of semilinear elliptic equations −div(aε(x)Duε=g(uε) with homogeneous Dirichlet boundary data, with respect to the G-convergence of the elliptic matrices aε. Here the function g has a subcritical or critical growth with respect to Sobolev imbedding.
DALL'AGLIO, Andrea, TCHOU N. A.
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Semilinear elliptic equations with additive noise
2017With temporal white noise, the solutions of stochastic parabolic equations have low regularity in time (Holder continuous with exponent 1∕2 −e and e > 0 is arbitrarily small) and thus the spectral approximation of Brownian motion leads to only half order convergence in its truncation mode n.
Zhongqiang Zhang, George Em Karniadakis
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New Creatinine- and Cystatin C–Based Equations to Estimate GFR without Race
New England Journal of Medicine, 2021Lesley A Inker+2 more
exaly
Generalized bioelectric impedance‐based equations underestimate body fluids in athletes
Scandinavian Journal of Medicine and Science in Sports, 2021Luís Sardinha+2 more
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Solving nonlinear fractional partial differential equations using the homotopy analysis method
Numerical Methods for Partial Differential Equations, 2010Abbas Saadatmandi+2 more
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Regularization of Grad’s 13 moment equations: Derivation and linear analysis
Physics of Fluids, 2003Henning Struchtrup, Manuel Torrilhon
exaly