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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1007/s10858-011-9600-7

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1432-0835

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Second order estimates for Hessian type fully nonl

Authors: Bo Guan Heming Jiao
Publish Date: 2015/05/30
Volume: 54, Issue: 3, Pages: 2693-2712
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Abstract

We derive a priori estimates for second order derivatives of solutions to a wide class of fully nonlinear elliptic equations on Riemannian manifolds There had been significant work in this direction especially in connection with important geometric problems and other applications but one had to make use of the special structures or needed extra assumptions which are more technical in nature to overcome various difficulties In this paper we are able to remove most of the technical assumptions and derive the estimates under conditions which are close to optimal These estimates enable one to prove existence results which are new even for bounded domains in Euclidean space

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  2. Fractional Poincaré inequality with finite total Q -curvature
  3. Solitary waves for a class of quasilinear Schrödinger equations in dimension two
  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
  5. On elliptic systems with Sobolev critical growth
  6. Critical points for functionals with quasilinear singular Euler–Lagrange equations
  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
  9. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
  10. Uniqueness and nondegeneracy of positive radial solutions of $$\mathbf {div\,{\varvec{(}}{\varvec{\rho }} \nabla u{\varvec{)}} +{\varvec{\rho }}{\varvec{(}}-gu+hu^p{\varvec{)}}=0}$$
  11. Lower bounds of Dirichlet eigenvalues for some degenerate elliptic operators
  12. Sharp energy estimates for nonlinear fractional diffusion equations
  13. On Newton equations which are totally integrable at infinity
  14. Energy asymptotics for Type II superconductors
  15. Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
  16. Singular points of Hölder asymptotically optimally doubling measures
  17. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
  19. A mean field type flow part I: compactness of solutions to a perturbed mean field type equation
  20. Boundary value problems for Willmore curves in $$\mathbb {R}^2$$
  21. Fractional eigenvalues
  22. On a quasilinear system involving the operator curl
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  24. Moser–Trudinger inequalities of vector bundle over a compact Riemannian manifold of dimension 2
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