Existence and non-existence results for harmonic maps between spheres

short-time existence and uniqueness of the solution. A new stability result for viscosity solutions of nonlinear para- bolic equations with weak convergence in time.

It is proved the existence of solutions to the exterior Dirichlet problem for the minimal hypersurface equation in complete non- compact Riemannian manifolds either with

J. WARNER, Curvature functions for compact 2-manifolds, Ann. KIESSLING, Statistical mechanics of classical particles with logarithmic interactions, Comm. PULVIRENTI,

In Section 4 we consider the case when Q has local maximum points in. We are only able to establish the existence of single-peaked solutions.. ld study their

DOUGLIS, The continuous dependance of generalized solutions of non linear partial differential equations upon initial data. FLEMING, The Cauchy problem for a non

The first non existence result for global minimizers of the Ginzburg-Landau energy with prescribed degrees p 6 = q and pq > 0 was obtained by Mironescu in [Mir13] following the

Thanks to [3], an existence result for the Yamabe problem in the singular setting is available in the more general context of pseudomanifolds and compact stratified spaces carrying

The next section is devoted to the derivation of addi- tional properties of weak solutions to (1.1) in the sense of Definition 1.2, including strong continuity with respect to