Fatou theorems for some nonlinear elliptic equations.
Generalized boundary value problems for nonlinear elliptic equations.
L²-data Dirichlet problem for weighted form Laplacians
We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.
Laplace type operators: Dirichlet problem
We investigate Laplace type operators in the Euclidean space. We give a purely algebraic proof of the theorem on existence and uniqueness (in the space of polynomial forms) of the Dirichlet boundary problem for a Laplace type operator and give a method of determining the exact solution to that problem. Moreover, we give a decomposition of the kernel of a Laplace type operator into -irreducible subspaces.
Large solutions for the laplacian with a power nonlinearity given by a variable exponent
Le rôle de la frontière dans un problème elliptique avec non-linéarité critique et conditions au bord de Neumann
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.
Maximum principle and existence of positive solutions for nonlinear systems involving degenerate -Laplacian operators.
Monogenic functions on surfaces.
Natural boundary value problems for weighted form laplacians
The four natural boundary problems for the weighted form Laplacians acting on polynomial differential forms in the -dimensional Euclidean ball are solved explicitly. Moreover, an algebraic algorithm for generating a solution from the boundary data is given in each case.
Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains.
Nonparametric minimal surfaces in whose boundaries have a jump discontinuity.
Nontrivial solutions for a robin problem with a nonlinear term asymptotically linear at and superlinear at .
Note on the Dirichlet problem with L2-Boundary Data.
Numerical treatment of 3-dimensional potential problem
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.
On a potential problem with incident wave as a field source
On the Boundary Behaviour of the Perron Generalized Solution.
On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
On the smoothness of solutions of variational inequalities with obstacles
On uniqueness of a solution of with given trace.