Strong maximum principle and boundary estimates for nonhomogeneous elliptic equations
NLP Lundström, M Olofsson, O Toivanen - arXiv preprint arXiv:2005.03338, 2020 - arxiv.org
NLP Lundström, M Olofsson, O Toivanen
arXiv preprint arXiv:2005.03338, 2020•arxiv.orgWe give a simple proof of the strong maximum principle for viscosity subsolutions of fully
nonlinear elliptic PDEs on the form $$ F (x, u, Du, D^ 2u)= 0$$ under suitable structure
conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of
smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and
that positive viscosity solutions vanishing on a portion of the boundary are comparable with
the distance function near the boundary. Our results apply to weak solutions of an …
nonlinear elliptic PDEs on the form $$ F (x, u, Du, D^ 2u)= 0$$ under suitable structure
conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of
smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and
that positive viscosity solutions vanishing on a portion of the boundary are comparable with
the distance function near the boundary. Our results apply to weak solutions of an …
We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form
under suitable structure conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply to weak solutions of an eigenvalue problem for the variable exponent -Laplacian.
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