Differentiability and partial Hölder continuity of the solutions of non-linear elliptic systems of order with quadratic growth
Differentiability for minimizers of anisotropic integrals
We consider a function , , minimizing the integral , , where , or some more general functional with the same behaviour; we prove the existence of second weak derivatives and .
Diffraction by convex bodies
Diffusion and cross-diffusion in pattern formation
We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
Diffusion and propagation problems in some ramified domains with a fractal boundary
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous...
Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.
Diffusion semigroups corresponding to uniformly elliptic divergence form operators
Dimension reduction for −Δ1
A 3D-2D dimension reduction for −Δ1 is obtained. A power law approximation from −Δp as p → 1 in terms of Γ-convergence, duality and asymptotics for least gradient functions has also been provided.
Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains
We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.
Dini-Campanato spaces and applications to nonlinear elliptic equations.
Direct and Inverse Error Estimates for Finite Elements With Mesh Refinements.
Dirichlet forms for general Wentzell boundary conditions, analytic semigroups, and cosine operator functions.
Dirichlet problem. Characterization of regularity.
Dirichlet problem for a linear elliptic equation in unbounded domains with -boundary data
Dirichlet problem for degenerate elliptic complex Monge-Ampère equation.
Dirichlet problem for quasi-linear elliptic equations.
Dirichlet problem with L-boundary data in contractible domains of Carnot groups
Let be a sub-laplacian on a stratified Lie group . In this paper we study the Dirichlet problem for with -boundary data, on domains which are contractible with respect to the natural dilations of . One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for . A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces.
Dirichlet problems for general Monge-Ampere equations.
Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains.
Dirichlet problems with singular and gradient quadratic lower order terms
We present a revisited form of a result proved in [Boccardo, Murat and Puel, Portugaliae Math.41 (1982) 507–534] and then we adapt the new proof in order to show the existence for solutions of quasilinear elliptic problems also if the lower order term has quadratic dependence on the gradient and singular dependence on the solution.