Besov regularity for solutions of p-harmonic equations
Advances in Nonlinear Analysis, 2017 We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., div𝒜(x,Du)=divF,{\operatorname{div}\mathcal{A}(x,Du)=\operatorname{div}F,} when 𝒜{\mathcal{A}} is a p-harmonic type ...
Clop Albert +2 more
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A note on boundary differentiability of solutions of nondivergece elliptic equations with unbounded drift [PDF]
arXiv, 2019 Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded ...
arxiv
Advances in Nonlinear Analysis, 2014 We address the regularity of solutions to elliptic and parabolic equations of the form -Δu+b·∇u=0${- \Delta u+b\cdot \nabla u=0}$ and ut-Δu+b·∇u=0${u_t- \Delta u+b\cdot \nabla u=0}$ with divergence-free drifts b.
Ignatova Mihaela
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Advances in Nonlinear Analysis, 2020 We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1 < p < 2 under controllable growth conditions, as well as natural growth conditions, respectively, in the Heisenberg group.
Wang Jialin +3 more
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Oscillating waves and optimal smoothing effect for one-dimensional nonlinear scalar conservation laws [PDF]
, 2012 Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for entropy solutions of nonlinear scalar conservations laws . In this short paper we will restrict our attention to the simpler one-dimensional case.
Castelli, Pierre, Junca, Stéphane
core +3 more sources
A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type [PDF]
arXiv, 2003 We establish Holder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.
arxiv
Fully nonlinear parabolic equations in two space variables [PDF]
arXiv, 2004 H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
arxiv
An example of $\infty$-harmonic function, which is not $C^2$ on a dense subset [PDF]
arXiv, 2004 We show that for certain boundary values McShane-Whitney's minimal-extension-like function is $\infty$-harmonic near the boundary and is not $C^2$ on a dense subset.
arxiv
Time-global smoothing estimates for a class of dispersive equations with constant coefficients [PDF]
arXiv, 2005 This paper has been withdrawn by the author due to an error.
arxiv
The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains [PDF]
arXiv, 2006 In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.
arxiv