## Published and Accepted Papers

New regularity estimates for fully nonlinear elliptic equations (with T. Nascimento) **J. Math. Pures Appl.** (9) 171 (2023), 1–25.

C1–regularity for degenerate diffusion equations. (with P. Andrade, D. Pellegrino, E. Pimentel) **Adv. Math.** 409 (2022), Paper No. 108667, 34 pp.

On the critical point regularity for degenerate diffusive equations. **Arch. Rational Mech. Anal. **244 (2022), no. 2, 293–316**.**

Fractional Sobolev regularity for fully nonlinear elliptic equations. (with E. Pimentel, M. Santos) Comm. Partial Differential Equations 47 (2022), no. 8, 1539–1558.

Optimal regularity for a two-phase free boundary problem ruled by the infinity Laplacian (with Araujo and Urbano), **Israel J. Math **245 (2021), no. 2, 773–785.

Geometric tangential analysis and sharp regularity for degenerate pdes. (with JM Urbano). Harnack inequalities and nonlinear operators, 175–192, **Springer INdAM Ser.**, 46, Springer, Cham, [2021], in honor of Prof. E. DiBenedetto.

Regularity theory for nonlinear diffusion processes. **Notices Amer. Math. Soc.** 67 (2020), no. 4, 475–483.

Free boundary problems involving singular weights (with J. Lamboley and Y. Sire). **Comm. Partial Differential Equations **45 (2020), no. 7, 758–775.

Optimal regularity for a two-phase free boundary problem ruled by the infinity Laplacian (with Araujo and Urbano), to appear in **Israel J. Math. **

Regularity of solutions to a class of variable-exponent fully nonlinear elliptic equations (with Bronze, Pimentel, and Rampasso). **J. Funct. Anal. **279 (2020), no. 12, 108781, 31 pp.

On the geometry of multilinear forms (with D. Pellegrino and W. Cavalcante). **Comm. Contemp. Math. **22 (2020), no. 2, 1950011, 26 pp.

On a continuous Gale–Berlekamp switching game (with Pellegrino, D. and Silva, J.), to appear in **An. Acad. Brasil. Ciênc.**

Reflexivity and nonweakly null maximizing sequences. (with Aron, R.; García, D. and Pellegrino, D.) ** Proc. Amer. Math. Soc. **148 (2020), no. 2, 741–750

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

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.

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

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

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.