## 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.