Hölder estimates for second-order operators on domains with rough boundary. (English) Zbl 1316.35110

The authors study mixed boundary value problems of elliptic type. Assuming only ellipticity condition on the coefficients and some weak conditions on the geometry of the domain, the Hölder continuity of the solution is shown.


35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
35A23 Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals
Full Text: Euclid