@misc{10481/59106, year = {2019}, month = {12}, url = {http://hdl.handle.net/10481/59106}, abstract = {We investigate the differences and similarities of the Dirichlet problem of the mean curvature equation in the Euclidean space and in the Lorentz-Minkowski space. Although the solvability of the Dirichlet problem follows standards techniques of elliptic equations, we focus in showing how the spacelike condition in the Lorentz-Minkowski space allows dropping the hypothesis on the mean convexity, which is required in the Euclidean case.}, organization = {This research was partially supported by grant No. MTM2017-89677-P,MINECO/AEI/FEDER, UE}, publisher = {MDPI}, keywords = {Euclidean space}, keywords = {Lorentz-Minkowski space}, keywords = {Dirichlet problem}, keywords = {Mean curvature}, keywords = {Maximum principle}, title = {The Dirichlet Problem of the Constant Mean Curvature in Equation in Lorentz-Minkowski Space and in Euclidean Space}, doi = {10.3390/math7121211}, author = {López Camino, Rafael}, }