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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Soit Ω un domaine borne dans R n avec n≥3. On etudie l'existence d'une fonction u satisfaisant l'equation elliptique non lineaire -Δu=u P +f(x,u) sur Ω, u>0 sur Ω, u=0 sur ∂Ω, ou p=(n+2)/(n−2),…
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Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
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Symmetry and related properties via the maximum principle
We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel…
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Partial regularity of suitable weak solutions of the navier‐stokes equations
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On functions of bounded mean oscillation
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First order interpolation inequalities with weights
Il existe une constante positive C telle que l'inegalite suivante est vraie pour tout u∈C 0 ∞ (R n ): ||X| G u| L r≤C||x|α|Du|| L p 2 ||x|βu| L q 1−a si et seulement si on a…
On elliptic partial differential equations
This series of lectures will touch on a number of topics in the theory of elliptic differential equations. In Lecture I we discuss the fundamental solution for equations with constant coefficients.…
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Symmetry of positive solutions of nonlinear elliptic equations in R
(1993). Radial symmetry of positive solutions of nonlinear elliptic equations in Rn. Communications in Partial Differential Equations: Vol. 18, No. 5-6, pp. 1043-1054.
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The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂Ω
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The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
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