可极化Carnot群上一类非散度型方程的非平凡解

§1Introduction WebeginbyquotingsomepreliminaryfactsontheCarnotgroupandreferthein estedreaderto[1-3]formorepreciseinformationonthissubject.ALiegroupG=(Rn,o)isaCarnotgroupifthefollowingproperties(G1)(G2)hold.(G1)RncanbesplitintorsubspacesRn=Rn1×...×Rnrandthedilations(δλdefinedbyδλ(x)=(λx(1),λ2x(2),...,λrx(r)),x(j)∈Rnj areautomorphismsofG.(G2)TheLiealgebragofGisgeneratedbytheleftinvariantvectorfieldsX1,.Xn1satisfying Xj(0)=xj,j=1,...,n1.Thenaturalnumbersrand Q=n1+2n2+...+rnr…     

Fundamental solutions for non-divergence form operators on stratified groups

We construct the fundamental solutions and for the non-divergence form operators and , where the 's are Hörmander vector fields generating a stratified group and is a positive-definite matrix with Hölder continuous entries. We also provide Gaussian estimates of and its derivatives and some results for the relevant Cauchy problem. Suitable long-time estimates of allow us to construct using both -saturation and approximation arguments.

     

Generalized solutions for a class of non-uniformaly elliptic equations in divergence form

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Multiplicity of positive solutions for a class of elliptic equations in divergence form

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Self-similar solutions for dyadic models of the Euler equations

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