Solvability of uniformly elliptic fully nonlinear PDE

B Sirakov - Archive for Rational Mechanics and Analysis, 2010 - Springer
We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic
fully nonlinear equations of the Hamilton–Jacobi–Bellman–Isaacs type with unbounded …

Alexandroff–Bakelman–Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

C Imbert - Journal of Differential Equations, 2011 - Elsevier
In this paper, we study fully non-linear elliptic equations in non-divergence form which can
be degenerate or singular when “the gradient is small”. Typical examples are either …

On the optimal L q-regularity for viscous Hamilton–Jacobi equations with subquadratic growth in the gradient

A Goffi - Communications in Contemporary Mathematics, 2024 - World Scientific
This paper studies a maximal L q-regularity property for nonlinear elliptic equations of
second order with a zeroth order term and gradient nonlinearities having superlinear and …

Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients

S Koike, A ŚWIĘCH - Journal of the Mathematical Society of Japan, 2009 - jstage.jst.go.jp
The weak Harnack inequality for Lp-viscosity solutions is shown for fully nonlinear, second
order uniformly elliptic partial differential equations with unbounded coefficients and …

Fundamental solutions of homogeneous fully nonlinear elliptic equations

SN Armstrong, CK Smart… - Communications on Pure …, 2011 - Wiley Online Library
We prove the existence of two fundamental solutions Φ and ̃Φ of the PDE\input amssym F
(D^ 2 Φ)= 0\rm in {R^ n ∖ {0\} for any positively homogeneous, uniformly elliptic operator F …

[HTML][HTML] C1, α regularity for fully nonlinear elliptic equations with superlinear growth in the gradient

G Nornberg - Journal de Mathématiques Pures et Appliquées, 2019 - Elsevier
We extend the Caffarelli-Świech-Winter C 1, α regularity estimates to L p-viscosity solutions
of fully nonlinear uniformly elliptic equations in nondivergence form with superlinear growth …

The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients

B Sirakov, P Souplet - Advances in Mathematics, 2021 - Elsevier
We develop a new, unified approach to the following two classical questions on elliptic
PDE:• the strong maximum principle for equations with non-Lipschitz nonlinearities,• the at …

Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients

JEM Braga, DR Moreira - Calculus of Variations and Partial Differential …, 2022 - Springer
In this paper, we prove up to the boundary gradient estimates for viscosity solutions to
inhomogeneous nonlinear Free Boundary Problems (FBP) governed by fully nonlinear and …

Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains

ME Amendola, L Rossi, A Vitolo - Abstract and Applied Analysis, 2008 - projecteuclid.org
We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient
term. We look for local estimates, such as weak Harnack inequality and local maximum …

Calderón–Zygmund estimates for the fully nonlinear obstacle problem with super-linear Hamiltonian terms and unbounded ingredients

JV da Silva, RT Frias - Mathematische Zeitschrift, 2024 - Springer
In this work, we show the existence/uniqueness of L p-viscosity solutions for a fully non-
linear obstacle problem with super-linear gradient growth, unbounded ingredients and …