Semilinear elliptic equations with singular nonlinearities

Boccardo, Lucio; Orsina, Luigi
March 2010
Calculus of Variations & Partial Differential Equations;Mar2010, Vol. 37 Issue 3/4, p363
Academic Journal
We prove existence, regularity and nonexistence results for problems whose model is with zero Dirichlet conditions on the boundary of an open, bounded subset Ω of $${\mathbb{R}^{N}}$$. Here γ > 0 and f is a nonnegative function on Ω. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of γ (which can be equal, larger or smaller than 1).


Related Articles

  • On some formulations of the Cauchy and Dirichlet problems. Tersenov, S. // Mathematical Notes;Feb2010, Vol. 87 Issue 1/2, p146 

    The article presents mathematical formulations of Cauchy and Dirichlet problems. It cites several mathematical conditions involving Caucy problems which include the parabolic system of equations, strips, and hyperbolic-type equation. It also notes a step-by-step formulation of Dirichlet problems...

  • The Dirichlet Problem for a Class of Quasilinear Elliptic Equation. Pengcheng Niu; Zixia Yuan // International Journal of Computational & Applied Mathematics;2007, Vol. 2 Issue 1, p43 

    The aim of this paper is to study solutions in Wloc1,p (Ω) ∩ C (...) for Dirichlet problem of p-Laplace equations (1 < p ≤ n)with nonhomogeneous term. Using the explicit construction of local barrier functions and Perron method, we prove the existence of solutions under the...

  • Solution of the Dirichlet problem for the Laplace equation for a multiply connected region with point symmetry. Spivak-Lavrov, I. F. // Technical Physics;Mar99, Vol. 44 Issue 3, p265 

    A method is proposed which uses an expansion of the potential in irreducible representations of the symmetry group of the field-defining elements of a system. A boundary-value problem is solved for multipole systems with planar plate electrodes for the C[sub nv] symmetry group. A quadrature...

  • Stationary configurations for the average distance functional and related problems. Buttazzo, Giuseppe; Mainini, Edoardo; Stepanov, Eugene // Control & Cybernetics;Dec2009, Vol. 38 Issue 4A, p1107 

    For a functional defined on the class of closed one-dimensional connected subsets of Rn we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied here are the average distance functional arising in the mass...

  • ON A SINGLE SOLVABILITY OF EQUATION λu -- ad2u + s~du = f, λ > 0, AND CONSTRUCTION OF NONLINEAR CONTRACTION SEMI GROUPS. Kukharchuk, M. M.; Yaremenko, M. I. // Naukovi visti NTUU - KPI;2007, Vol. 2007 Issue 5, p148 

    The work is devoted to investigation of the second-order quasi-linear elliptic equations with slow-increasing coefficients on the Euclidean space R¹, 1 ≥ 3. The authors reject a traditional point of view at the admissible class of generalized solutions of the second-order elliptic...

  • A Class of Singularly Perturbed Generalized Boundary Value Problems for Quasi-Linear Elliptic Equation of Higher Order. Jia-qi Mo; Cheng Ouyang // Applied Mathematics & Mechanics;Mar2001, Vol. 22 Issue 3, p372 

    The singularly perturbed generalized boundary value problems for the quasi-linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied.

  • Solution of Laplace’s equation in plane single-connected regions bounded by arbitrary single curves. Minotti, F.; Moreno, C. // Journal of Mathematical Physics;Aug90, Vol. 31 Issue 8, p1914 

    A method is developed to solve Laplace’s equation with Dirichlet’s or Neumann’s conditions in plane, single-connected regions bounded by arbitrary single curves. It is based on the existence of a conformal transformation that reduces the original problem to another whose...

  • Characterization of Generating Ideals in Some Rings of Entire Functions. Abanin, A. V.; Shabarshina, I. S. // Mathematical Notes;Sep/Oct2003, Vol. 74 Issue 3/4, p459 

    Let E be a ring of entire functions on \Bbb C^N with the operation of pointwise multiplication, and let f_1,\dots,f_m be a set of nonzero elements in E. The ideal E(f_1,\dots,f_m) in E with generators...

  • Vanishing and non-vanishing Dirichlet twists of L-functions of elliptic curves. Fearnley, Jack; Kisilevsky, Hershy; Kuwata, Masato // Journal of the London Mathematical Society;Oct2012, Vol. 86 Issue 2, p539 

    Let L(E/ℚ, s) be the L-function of an elliptic curve E defined over the rational field ℚ. We examine the vanishing and non-vanishing of the central values L(E, 1, χ) of the twisted L-function as χ ranges over Dirichlet characters of a given order.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics