Uniform Estimates in Periodic Homogenization of Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s00205-021-01745-1
Abstract: This article is concerned with uniform $$C^{1,\alpha }$$ C 1 , α and $$C^{1,1}$$ C 1 , 1 estimates in periodic homogenization of fully nonlinear elliptic equations. The analysis is based on the compactness method,… read more here.
Keywords: estimates periodic; fully nonlinear; homogenization; periodic homogenization ... See more keywords
Global $$W^{2,\delta }$$W2,δ estimates for a type of singular fully nonlinear elliptic equations
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DOI: 10.1007/s00209-016-1743-5
Abstract: We obtain global $$W^{2,\delta }$$W2,δ estimates for a type of singular fully nonlinear elliptic equations where the right hand side term belongs to $$L^\infty $$L∞. The main idea of the proof is to slide paraboloids… read more here.
Keywords: fully nonlinear; global delta; type singular; delta estimates ... See more keywords
Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s00220-019-03370-2
Abstract: In this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with coefficients and right hand sides (RHS) in Lq… read more here.
Keywords: regularity convex; fully nonlinear; regularity; elliptic equations ... See more keywords
Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs
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DOI: 10.1007/s00440-018-0859-4
Abstract: In this article, we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of the solution under a Lipschitz type assumption on the… read more here.
Keywords: nonlinear stochastic; fully nonlinear; stochastic pdes; probabilistic interpretation ... See more keywords
Higher-Order Adaptive Finite Difference Methods for Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s10915-017-0586-5
Abstract: We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for adaptive meshes and complicated… read more here.
Keywords: fully nonlinear; difference; difference methods; higher order ... See more keywords
The Brunn–Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators
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DOI: 10.1016/j.aim.2019.106855
Abstract: Abstract We prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequality on the class of open bounded sets in R… read more here.
Keywords: fully nonlinear; nonlinear homogeneous; brunn minkowski; eigenvalue fully ... See more keywords
On the fully nonlinear water entry of a cone in Stokes wave
Sign Up to like & getrecommendations! Published in 2019 at "Engineering Analysis with Boundary Elements"
DOI: 10.1016/j.enganabound.2018.10.019
Abstract: Abstract Motivated by the wave entry problems of the three-dimensional (3D) ship bow, the paper concentrates on the interaction between an incident wave and a falling cone. The nonlinear 5th order Stokes wave is used… read more here.
Keywords: entry; fully nonlinear; cone; stokes wave ... See more keywords
Investigation on responses and wave climbing of a ship in large waves using a fully nonlinear boundary element method
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DOI: 10.1016/j.enganabound.2021.02.002
Abstract: Abstract In this study, a fully nonlinear method, in the time domain, is used to simulate ship motion caused by large waves, and the problem of wave climbing along the freeboard in large waves is… read more here.
Keywords: ship; fully nonlinear; method; large waves ... See more keywords
A study on fully nonlinear wave load effects on floating wind turbine
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DOI: 10.1016/j.jfluidstructs.2019.05.008
Abstract: Abstract The influence of fully nonlinear wave effects on floating wind turbine has been studied in this paper by comparing both floater motions and structural responses of tower base and mooring lines exposed to linear… read more here.
Keywords: nonlinear wave; fully nonlinear; wind turbine; floating wind ... See more keywords
Symmetry results for viscosity solutions of fully nonlinear equations in annular and exterior domains
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DOI: 10.1016/j.jmaa.2019.123776
Abstract: Abstract In this paper, we prove the symmetry and monotonicity results of viscosity solutions for fully nonlinear elliptic equations F ( D 2 u , D u , u , x ) = 0 and… read more here.
Keywords: fully nonlinear; exterior domains; solutions fully; equations annular ... See more keywords
Hessian estimates for fully nonlinear equations via the large-M-inequality principle
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DOI: 10.1016/j.jmaa.2020.123953
Abstract: Abstract The approach using the large-M-inequality principle introduced by Acerbi and Mingione [2] has been broadly used in W 1 , p -regularity theory for nonlinear equations in divergence form. We apply this approach to… read more here.
Keywords: fully nonlinear; large inequality; hessian estimates; nonlinear equations ... See more keywords