文摘
In this paper we investigate the existence of rotationally symmetric entire graphs (resp. entire spacelike graphs) with prescribed k -th mean curvature function in Euclidean space class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630525X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1630525X&_rdoc=1&_issn=0022247X&md5=393b8281c47326de44685831265a4686" title="Click to view the MathML source">Rn+1class="mathContainer hidden">class="mathCode"> (resp. Minkowski spacetime class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630525X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1630525X&_rdoc=1&_issn=0022247X&md5=fd4cd44e2fa510bd454d3fb87a19f504" title="Click to view the MathML source">Ln+1class="mathContainer hidden">class="mathCode">). As a previous step, we analyze the associated homogeneous Dirichlet problem on a ball, which is not elliptic for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1630525X&_mathId=si3.gif&_user=111111111&_pii=S0022247X1630525X&_rdoc=1&_issn=0022247X&md5=5fe743fb6e1520d1b387928142b9a762" title="Click to view the MathML source">k>1class="mathContainer hidden">class="mathCode">, and then we prove that it is possible to extend the solutions. Moreover, a sufficient condition for uniqueness is given in both cases.