# Publications

## Published and Accepted Papers

Towards the Cp′ regularity conjecture in higher dimensions. (with D. Araujo and JM Urbano).  Int. Math. Res. Not. 2018, no. 20, 6481–6495.

On the geometry of multilinear forms (with D. Pellegrino and W. Cavalcante). To appear in Comm. Contemp. Math.

Nonlinear diffusive problems: geometric insights and beyond. Intelligencer 2018

Geometric tangential analysis and sharp regularity for degenerate pdes. (with JM Urbano). To appear in Proceedings of the INdAM Meeting “Harnacks Inequalities and Nonlinear Operators” in honor of Prof. E. DiBenedetto.

A proof of the Cp′ regularity conjecture in the plane. (with D. Araujo and JM Urbano) Adv. Math. 316 (2017), 541–553.

Nonlinear elliptic equations with high order singularities.  Potential Anal. 48 (2018), no. 3, 325–335.

Regularity principle in sequence spaces and applications. (with D. Pellegrino, J. Santos, D. Serrano-Rodriquez). Bull. Sci. Math. 141 (2017), no. 8, 802–837.

Sharp regularity estimates for second order fully nonlinear parabolic equations. (with JV Silva).  Math. Ann. 369 (2017), no. 3-4, 1623–1648

Towards sharp Bohnenblust–Hille constants. (with D. Pellegrino). Comm. Contemp. Math. 20 (2018), no. 3, 1750029, 33 pp

Singularly perturbed equations of degenerate type. (with D. Araujo & G. Ricarte). Ann. Inst. H. Poincare Anal. Non Lineaire. 34 (2017), no. 3, 655–678.

Global Monge-Ampere equations with asymptotically periodic data. (with L. Zhang). Indiana Univ. Math. J. 65 No. 2 (2016), 399–422.

Sharp hessian integrability estimates for nonlinear elliptic equations: an asymptotic approach. (with E. Pimentel). J. Math. Pures Appl. 106 (2016), pp. 744–767.

Infinity Laplacian equation with strong absorptions. (with. D. Araujo e R. Leitao). J. Funct. Anal. 270 (2016), pp. 2249–2267.

Cavity problems in discontinuous media. (with. D. dos Prazeres). Calc. Var. Partial Differential Equations. 55 (2016), no. 1, 55:10.

Regularity for the fully nonlinear dead-core problem. Math. Ann. 364 (2016), no. 3-4, 1121–1134.

Optimal design problems with fractional diffusion. (with R. Teymurazyan). J. London Math. Soc. (2) 92 (2015), no. 2, 338–352.

Asymptotics and regularity for flat solutions to fully nonlinear elliptic problems. (with D. dos Prazeres). Ann. Sc. Norm. Super. Pisa Cl. Sci. Vol. XV (2016), 485—500.

Free transmission problems. (with M. Amaral). Comm. Math. Phys. 337 (2015), no. 3, 1465–1489.

Regularity for degenerate two-phase free boundary problems. (with R. Leitao & O. Queiroz). Ann. Inst. H. Poincare Anal. Non Lineaire. 32 (2015), pp. 741–762

Hessian continuity at degenerate points in nonvariational elliptic problems. Int. Math. Res. Not. (2015) Vol. 2015 6893–6906.

Geometric gradient estimates for solutions to degenerate elliptic equations. (with D. Araujo & G. Ricarte). Calc. Var. Partial Differential Equations. 53 (2015), no. 3-4, 605–625.

Optimal regularity at the free boundary for the infinity obstacle problem. (with J. Rossi & J.M. Urbano). Interfaces Free Bound. 7 (2015), 381–398.

Regularity estimates for fully non linear elliptic equations which are asymptotically convex. (with L. Silvestre). Contributions to Nonlinear Elliptic Equations and Systems, Volume 86 of the series Progr. Nonlinear Differential Equations Appl. pp 425-438.

Geometric regularity estimates for elliptic equations. Proceedings of the MCA 2013. Contemp. Math. 656 (2016) 185–204.

Regularity for quasilinear equations on degenerate singular sets. Math. Ann. 358 (2014), no 1, 241–256.

Universal moduli of continuity for solutions to fully nonlinear elliptic equations. Arch. Rational Mech. Anal. 211 (2014), no 3, 911–927.

A geometric tangential approach to sharp regularity for degenerate evolution equations. (with J.M. Urbano) Anal. PDE. Vol. 7, No 3 (2014), 733–744.

An intrinsic Liouville theorem for degenerate parabolic equations. (with J.M. Urbano) Arch. Math. 102 (2014), 483-487.

Regularity and geometric estimates for minima of discontinuous functionals. (with R. Leitao) Rev. Mat. Iberoam. 31 (2015), no. 1, 69–108.

Geometric approach to nonvariational singular elliptic equations. (with D. Araujo) Arch. Rational Mech. Anal. 209 (2013), no 3, 1019–1054.

Sharp regularity for general Poisson equations with borderline sources. J. Math. Pures Appl. (9) 99 (2013), no. 2, 150–164.

A limiting free boundary problem ruled by Aronsson’s equation. (with J. Rossi). Trans. Amer. Math. Soc. 364 (2012), 703-719.

An elliptic variational problem involving level surface area on Riemannian manifolds. (with L. Zhang). Rev. Mat. Iberoam. 28 (2012), no. 3, 759-772.

Monotonicity theorems for Laplace Beltrami operator on Riemannian manifolds. (with L. Zhang). Adv. Math. , 226, (2011), no 2, pp. 1259-1284.

Existence and regularity properties of non-isotropic singular elliptic equations. (with M. Montenegro and O. Queiroz). Math. Ann. , 351 (1), (2011) pg. 215-250.

Fully nonlinear singularly perturbed equations and asymptotic free boundaries. (with G. Ricarte). J. Funct. Anal. , 261, no 6 (2011), 1624-1673.

A local parabolic monotonicity formula on Riemannian manifolds. (with L. Zhang). J. Geom. Anal. , Vol 21, No 3 (2011) 513–526.

Asymptotic behavior of solutions to the $\sigma_k$-Yamabe equation near isolated singularities. (with Z. Han & Y. Li). Invent. Math. , 182, No. 3, 635-684 (2010).

Optimal design problems in rough inhomogeneous media. Existence theory. Amer. J. Math. , Vol 132, No 6 (2010) pp. 1445-1492.

Gradient estimates for viscosity solutions of singular fully non-linear elliptic equations. (with M. Montenegro). J. Funct. Anal. 259 (2010) 428-452.

Regularity for obstacle problems in infinite dimensional Hilbert spaces. (with A. Swiech). Adv. Math 259 (2010) 428-452.

Norm optimization problem for linear operators in classical Banach spaces. (with D. Pellegrino). Bull. Braz. Math. Soc. , 30 (2009), no 3, 417–431.

A variational treatment for elliptic equations of the flame propagation type: regularity of the free boundary. Ann. Inst. H. Poincare Anal. Non Lineaire, 25 (2008), pp. 633-658.

A singular perturbation free boundary problem for elliptic equations in divergence form. (with D. Moreira). Calc. Var. Partial Differential Equations 29 (2007), no 2, 161–190.

On infinite order and fully nonlinear partial differential evolution equations. J. Differential Equations 238 (2007), no 1, 43–63.

Uniqueness, symmetry and full regularity of free boundary in optimization problems with volume constraints. Interface Free Bound 9 (2007), 133–148.

Optimal regularity of viscosity solutions of fully nonlinear singular equations and their limiting free boundary problems. Mat. Contemp 30 (2006), 217–237.

An optimization problem with free boundary governed by a degenerate quasilinear operator. (with K. Oliveira). Differential and Integral Equations 19 (2006), no. 9, 1061–1080.

The nonlinear optimization problem in heat conduction. Calc. Var. Partial Differential Equations 24 (2005), no. 1, 21–46.

Strong solutions for differential equations in abstract spaces. J. Differential Equations 214 (2005), no. 1, 65–91.

On the behavior of weak convergence under nonlinearities and applications. (with D. Moreira) Proc. Amer. Math. Soc. 133 (2005), no. 6, 1647–1656.

A topological and geometric approach to fixed points results for sum of operators and applications. (with C. Barroso) Nonlinear Anal. 60 (2005), no. 4, 625–650.

Weak convergence under nonlinearities. (with D. Moreira) An. Acad. Brasil. Ciienc. 75 (2003) no. 1, 9–19.

## Pre Prints

Optimal regularity for a two-phase free boundary problem ruled by the infinity Laplacian (with Araujo and Urbano).

Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations (with Bronze, Pimentel, and Rampasso).

Reflexivity and non-weakly null maximizing sequences (with Aron, Garcia and Pellegrino).

Optimal regularity for a two-phase free boundary problem ruled by the infinity Laplacian (with D. Araujo and JM Urbano)

Free boundary problems involving singular weights (with J. Lamboley and Y. Sire).

Free boundary problems: A Primer (book project sponsored by De Gruyter publishing house).