Regularity of solutions to fully nonlinear elliptic and parabolic free boundary problems

• We consider fully nonlinear obstacle-type problems of the form. F(D2u,x)=f(x)a.e. in B1∩Ω,|D2u|≤Ka.e. in B1\Ω, where Ω is an open set and K>0. In particular, structural conditions on F are presented which ensure that W2,n(B1) solutions achieve the optimal C1,1(B1/2) regularity when f is Hölder continuous. Moreover, if f is positive on B-1, Lipschitz continuous, and u≠0⊂Ω, we obtain interior C1 regularity of the free boundary under a uniform thickness assumption on u=0. Lastly, we extend these results to the parabolic setting.

Ämnesord

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Nonlinear elliptic equations

Nonlinear parabolic equations

Free boundaries

Regularity theory

Obstacle problems

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