Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients

Autor(es)

da Silva, Joao Vitor ^[1] ; Nornberg, Gabrielle ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, IMECC, Dept Matemat, Campinas - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS; v. 60, n. 6 DEC 2021.
• Citações Web of Science: 0

Resumo

We develop an optimal regularity theory for L-p-viscosity solutions of fully nonlinear uniformly elliptic equations in nondivergence form whose gradient growth is described through a Hamiltonian function with measurable and possibly unbounded coefficients. Our approach treats both superlinear and sublinear gradient regimes in a unified way. We show C-0,C-alpha, C-0,C-Log-Lip, C-1,C-alpha, C-1,C-Log-Lip and C-2,C-alpha regularity estimates, by displaying the growth allowed to the Hamiltonian in order to deal with an unbounded nonlinear gradient coefficient, whose integrability in turn gets worse as we approach the quadratic regime. These results may be seen as natural extensions of Teixeira (Arch Ration Mech Anal 211(3):911-927, 2014) and Nornberg (J Math Pures Appl 128(9):297-329, 2019). Moreover, we find proper compatibility conditions for which our regularity results depend intrinsically on the integrability of the underlying source term. As a byproduct of our methods, we prove a priori BMO estimates; sharp regularity to associated recession and flat profiles under relaxed convexity assumptions; improved regularity for a class of singular PDEs; and a Perron type result under unbounded ingredients. (AU)

• Processo FAPESP: 18/04000-9 - Existência e multiplicidade de soluções para problemas elípticos com crescimento quadrático no gradiente
• Beneficiário: Gabrielle Saller Nornberg
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 19/03101-9 - Simetria e existência de soluções para problemas elípticos não-lineares
• Beneficiário: Gabrielle Saller Nornberg
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado